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<p>Last updated on<strong>September 26, 2025</strong></p>
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<p>Last updated on<strong>September 26, 2025</strong></p>
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<p>In trigonometry, the primary functions are sine (sin), cosine (cos), and tangent (tan). These functions relate the angles and sides of a right triangle. In this topic, we will learn the formulas for sin, cos, and tan.</p>
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<p>In trigonometry, the primary functions are sine (sin), cosine (cos), and tangent (tan). These functions relate the angles and sides of a right triangle. In this topic, we will learn the formulas for sin, cos, and tan.</p>
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<h2>List of Math Formulas for Sin, Cos, and Tan</h2>
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<h2>List of Math Formulas for Sin, Cos, and Tan</h2>
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<p>The primary trigonometric<a>functions</a>are sine, cosine, and tangent. Let’s learn the<a>formula</a>to calculate sin, cos, and tan.</p>
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<p>The primary trigonometric<a>functions</a>are sine, cosine, and tangent. Let’s learn the<a>formula</a>to calculate sin, cos, and tan.</p>
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<h2>Math formula for Sin</h2>
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<h2>Math formula for Sin</h2>
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<p>The sine<a>of</a>an angle in a right triangle is the<a>ratio</a>of the length of the opposite side to the length of the hypotenuse.</p>
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<p>The sine<a>of</a>an angle in a right triangle is the<a>ratio</a>of the length of the opposite side to the length of the hypotenuse.</p>
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<p>It is calculated using the formula: sin(θ) = opposite/hypotenuse</p>
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<p>It is calculated using the formula: sin(θ) = opposite/hypotenuse</p>
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<h2>Math formula for Cos</h2>
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<h2>Math formula for Cos</h2>
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<p>The cosine of an angle in a right triangle is the ratio of the length of the adjacent side to the length of the hypotenuse.</p>
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<p>The cosine of an angle in a right triangle is the ratio of the length of the adjacent side to the length of the hypotenuse.</p>
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<p>It is calculated using the formula: cos(θ) = adjacent/hypotenuse</p>
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<p>It is calculated using the formula: cos(θ) = adjacent/hypotenuse</p>
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<h2>Math formula for Tan</h2>
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<h2>Math formula for Tan</h2>
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<p>The tangent of an angle in a right triangle is the ratio of the length of the opposite side to the length of the adjacent side.</p>
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<p>The tangent of an angle in a right triangle is the ratio of the length of the opposite side to the length of the adjacent side.</p>
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<p>It is calculated using the formula: tan(θ) = opposite/adjacent</p>
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<p>It is calculated using the formula: tan(θ) = opposite/adjacent</p>
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<h2>Importance of Sin, Cos, and Tan Formulas</h2>
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<h2>Importance of Sin, Cos, and Tan Formulas</h2>
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<p>In<a>math</a>and real life, we use the sin, cos, and tan formulas to analyze and solve problems involving right triangles.</p>
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<p>In<a>math</a>and real life, we use the sin, cos, and tan formulas to analyze and solve problems involving right triangles.</p>
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<p>Here are some important points about sin, cos, and tan:</p>
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<p>Here are some important points about sin, cos, and tan:</p>
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<ul><li>These functions help in calculating angles and sides in<a>trigonometry</a>. </li>
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<ul><li>These functions help in calculating angles and sides in<a>trigonometry</a>. </li>
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<li>By learning these formulas, students can easily understand concepts like wave functions, oscillations, and even some aspects of<a>calculus</a>. </li>
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<li>By learning these formulas, students can easily understand concepts like wave functions, oscillations, and even some aspects of<a>calculus</a>. </li>
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<li>To find distances or heights indirectly, we often use these trigonometric<a>ratios</a>.</li>
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<li>To find distances or heights indirectly, we often use these trigonometric<a>ratios</a>.</li>
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</ul><h2>Tips and Tricks to Memorize Sin, Cos, and Tan Math Formulas</h2>
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</ul><h2>Tips and Tricks to Memorize Sin, Cos, and Tan Math Formulas</h2>
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<p>Students often find trigonometry formulas tricky and confusing.</p>
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<p>Students often find trigonometry formulas tricky and confusing.</p>
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<p>Here are some tips and tricks to master the sin, cos, and tan formulas:</p>
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<p>Here are some tips and tricks to master the sin, cos, and tan formulas:</p>
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<ul><li>Use simple mnemonics like SOH-CAH-TOA, which stands for Sine = Opposite/Hypotenuse, Cosine = Adjacent/Hypotenuse, Tangent = Opposite/Adjacent. </li>
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<ul><li>Use simple mnemonics like SOH-CAH-TOA, which stands for Sine = Opposite/Hypotenuse, Cosine = Adjacent/Hypotenuse, Tangent = Opposite/Adjacent. </li>
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<li>Connect the use of sin, cos, and tan with real-life scenarios like ramps, ladders, or shadows. </li>
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<li>Connect the use of sin, cos, and tan with real-life scenarios like ramps, ladders, or shadows. </li>
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<li>Use flashcards to memorize the formulas and rewrite them for quick recall, and create a formula chart for quick reference.</li>
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<li>Use flashcards to memorize the formulas and rewrite them for quick recall, and create a formula chart for quick reference.</li>
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</ul><h2>Common Mistakes and How to Avoid Them While Using Sin, Cos, and Tan Math Formulas</h2>
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</ul><h2>Common Mistakes and How to Avoid Them While Using Sin, Cos, and Tan Math Formulas</h2>
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<p>Students make errors when calculating sin, cos, and tan.</p>
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<p>Students make errors when calculating sin, cos, and tan.</p>
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<p>Here are some mistakes and the ways to avoid them, to master them.</p>
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<p>Here are some mistakes and the ways to avoid them, to master them.</p>
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<h3>Problem 1</h3>
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<h3>Problem 1</h3>
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<p>What is the sin of an angle θ if the opposite side is 3 and the hypotenuse is 5?</p>
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<p>What is the sin of an angle θ if the opposite side is 3 and the hypotenuse is 5?</p>
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<p>Okay, lets begin</p>
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<p>Okay, lets begin</p>
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<p>The sin(θ) is 0.6</p>
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<p>The sin(θ) is 0.6</p>
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<h3>Explanation</h3>
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<h3>Explanation</h3>
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<p>To find sin(θ), use the formula: sin(θ) = opposite/hypotenuse = 3/5 = 0.6</p>
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<p>To find sin(θ), use the formula: sin(θ) = opposite/hypotenuse = 3/5 = 0.6</p>
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<p>Well explained 👍</p>
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<p>Well explained 👍</p>
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<h3>Problem 2</h3>
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<h3>Problem 2</h3>
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<p>Find the cos of an angle θ if the adjacent side is 4 and the hypotenuse is 5?</p>
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<p>Find the cos of an angle θ if the adjacent side is 4 and the hypotenuse is 5?</p>
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<p>Okay, lets begin</p>
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<p>Okay, lets begin</p>
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<p>The cos(θ) is 0.8</p>
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<p>The cos(θ) is 0.8</p>
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<h3>Explanation</h3>
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<h3>Explanation</h3>
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<p>To find cos(θ), use the formula: cos(θ) = adjacent/hypotenuse = 4/5 = 0.8</p>
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<p>To find cos(θ), use the formula: cos(θ) = adjacent/hypotenuse = 4/5 = 0.8</p>
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<p>Well explained 👍</p>
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<p>Well explained 👍</p>
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<h3>Problem 3</h3>
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<h3>Problem 3</h3>
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<p>What is the tan of an angle θ if the opposite side is 5 and the adjacent side is 12?</p>
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<p>What is the tan of an angle θ if the opposite side is 5 and the adjacent side is 12?</p>
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<p>Okay, lets begin</p>
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<p>Okay, lets begin</p>
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<p>The tan(θ) is 0.4167</p>
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<p>The tan(θ) is 0.4167</p>
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<h3>Explanation</h3>
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<h3>Explanation</h3>
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<p>To find tan(θ), use the formula: tan(θ) = opposite/adjacent = 5/12 ≈ 0.4167</p>
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<p>To find tan(θ), use the formula: tan(θ) = opposite/adjacent = 5/12 ≈ 0.4167</p>
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<p>Well explained 👍</p>
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<p>Well explained 👍</p>
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<h3>Problem 4</h3>
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<h3>Problem 4</h3>
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<p>A ladder leans against a wall, making an angle of 60° with the ground. If the ladder is 10 meters long, what is the height it reaches on the wall?</p>
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<p>A ladder leans against a wall, making an angle of 60° with the ground. If the ladder is 10 meters long, what is the height it reaches on the wall?</p>
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<p>Okay, lets begin</p>
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<p>Okay, lets begin</p>
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<p>The height is 8.66 meters</p>
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<p>The height is 8.66 meters</p>
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<h3>Explanation</h3>
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<h3>Explanation</h3>
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<p>Using sin(60°) = opposite/hypotenuse = height/10 Height = 10 * sin(60°) = 10 * 0.866 = 8.66 meters</p>
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<p>Using sin(60°) = opposite/hypotenuse = height/10 Height = 10 * sin(60°) = 10 * 0.866 = 8.66 meters</p>
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<p>Well explained 👍</p>
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<p>Well explained 👍</p>
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<h3>Problem 5</h3>
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<h3>Problem 5</h3>
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<p>A ramp is inclined at 30° to the horizontal. If the length of the ramp is 5 meters, what is the horizontal distance covered by the ramp?</p>
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<p>A ramp is inclined at 30° to the horizontal. If the length of the ramp is 5 meters, what is the horizontal distance covered by the ramp?</p>
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<p>Okay, lets begin</p>
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<p>Okay, lets begin</p>
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<p>The horizontal distance is 4.33 meters</p>
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<p>The horizontal distance is 4.33 meters</p>
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<h3>Explanation</h3>
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<h3>Explanation</h3>
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<p>Using cos(30°) = adjacent/hypotenuse = horizontal distance/5 Horizontal distance = 5 * cos(30°) = 5 * 0.866 = 4.33 meters</p>
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<p>Using cos(30°) = adjacent/hypotenuse = horizontal distance/5 Horizontal distance = 5 * cos(30°) = 5 * 0.866 = 4.33 meters</p>
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<p>Well explained 👍</p>
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<p>Well explained 👍</p>
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<h2>FAQs on Sin, Cos, Tan Math Formulas</h2>
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<h2>FAQs on Sin, Cos, Tan Math Formulas</h2>
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<h3>1.What is the formula for sin?</h3>
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<h3>1.What is the formula for sin?</h3>
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<p>The formula to find sin is: sin(θ) = opposite/hypotenuse</p>
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<p>The formula to find sin is: sin(θ) = opposite/hypotenuse</p>
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<h3>2.What is the formula for cos?</h3>
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<h3>2.What is the formula for cos?</h3>
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<p>The formula for cos is: cos(θ) = adjacent/hypotenuse</p>
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<p>The formula for cos is: cos(θ) = adjacent/hypotenuse</p>
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<h3>3.How to find tan?</h3>
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<h3>3.How to find tan?</h3>
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<p>To find tan of an angle, use the formula: tan(θ) = opposite/adjacent</p>
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<p>To find tan of an angle, use the formula: tan(θ) = opposite/adjacent</p>
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<h3>4.What is the tan of an angle if the opposite side is 7 and the adjacent side is 24?</h3>
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<h3>4.What is the tan of an angle if the opposite side is 7 and the adjacent side is 24?</h3>
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<h3>5.What is the sin of 45°?</h3>
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<h3>5.What is the sin of 45°?</h3>
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<p>The sin of 45° is √2/2 or approximately 0.7071</p>
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<p>The sin of 45° is √2/2 or approximately 0.7071</p>
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<h2>Glossary for Sin, Cos, and Tan Math Formulas</h2>
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<h2>Glossary for Sin, Cos, and Tan Math Formulas</h2>
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<ul><li><strong>Sine (sin):</strong>A trigonometric function that represents the ratio of the opposite side to the hypotenuse of a right triangle.</li>
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<ul><li><strong>Sine (sin):</strong>A trigonometric function that represents the ratio of the opposite side to the hypotenuse of a right triangle.</li>
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</ul><ul><li><strong>Cosine (cos):</strong>A trigonometric function that represents the ratio of the adjacent side to the hypotenuse of a right triangle.</li>
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</ul><ul><li><strong>Cosine (cos):</strong>A trigonometric function that represents the ratio of the adjacent side to the hypotenuse of a right triangle.</li>
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</ul><ul><li><strong>Tangent (tan):</strong>A trigonometric function that represents the ratio of the opposite side to the adjacent side of a right triangle.</li>
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</ul><ul><li><strong>Tangent (tan):</strong>A trigonometric function that represents the ratio of the opposite side to the adjacent side of a right triangle.</li>
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</ul><ul><li><strong>Hypotenuse:</strong>The longest side of a right triangle, opposite the right angle.</li>
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</ul><ul><li><strong>Hypotenuse:</strong>The longest side of a right triangle, opposite the right angle.</li>
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</ul><ul><li><strong>Trigonometry:</strong>A branch of mathematics that studies relationships involving lengths and angles of triangles.</li>
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</ul><ul><li><strong>Trigonometry:</strong>A branch of mathematics that studies relationships involving lengths and angles of triangles.</li>
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</ul><h2>Jaskaran Singh Saluja</h2>
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</ul><h2>Jaskaran Singh Saluja</h2>
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<h3>About the Author</h3>
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<h3>About the Author</h3>
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<p>Jaskaran Singh Saluja is a math wizard with nearly three years of experience as a math teacher. His expertise is in algebra, so he can make algebra classes interesting by turning tricky equations into simple puzzles.</p>
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<p>Jaskaran Singh Saluja is a math wizard with nearly three years of experience as a math teacher. His expertise is in algebra, so he can make algebra classes interesting by turning tricky equations into simple puzzles.</p>
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<h3>Fun Fact</h3>
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<h3>Fun Fact</h3>
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<p>: He loves to play the quiz with kids through algebra to make kids love it.</p>
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<p>: He loves to play the quiz with kids through algebra to make kids love it.</p>