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Sin A, cos A and tan A

Sin A, cos A, and tan A are the basic trigonometric ratios formed from the opposite, adjacent, and hypotenuse sides of a right triangle.

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Student-friendly explanation

These three ratios are the starting point of the chapter. Sine uses opposite over hypotenuse, cosine uses adjacent over hypotenuse, and tangent uses opposite over adjacent. If the sides are identified correctly, the ratio becomes simple and direct.

How to write this in exams

  1. 1

    Start with the exact idea

    Sin A, cos A, and tan A are the basic trigonometric ratios formed from the opposite, adjacent, and hypotenuse sides of a right triangle.

  2. 2

    Then show how to use it

    1. Choose the angle. 2. Label the three sides correctly. 3. Pick the ratio you need. 4. Substitute the lengths. 5. Simplify the fraction if needed.

  3. 3

    Add one concrete example

    If for angle A the opposite side is 4 cm, adjacent side is 3 cm, and hypotenuse is 5 cm, then sin A = 4/5, cos A = 3/5, and tan A = 4/3.

  4. 4

    Avoid this incomplete answer

    A common wrong answer is to use the wrong side order in tangent. That gives the reciprocal ratio and changes the answer completely.

Definition

Sin A, cos A, and tan A are the basic trigonometric ratios formed from the opposite, adjacent, and hypotenuse sides of a right triangle.

Example

If for angle A the opposite side is 4 cm, adjacent side is 3 cm, and hypotenuse is 5 cm, then sin A = 4/5, cos A = 3/5, and tan A = 4/3.

Rule to remember

sin A = opposite/hypotenuse, cos A = adjacent/hypotenuse, tan A = opposite/adjacent.

Memory hook

Sine and cosine keep the hypotenuse in the denominator; tangent stays in the triangle.

Examples and method

Worked example

For angle A, if opposite = 6 cm and adjacent = 8 cm, then tan A = 6/8 = 3/4 after simplification.

Method to apply

1. Choose the angle. 2. Label the three sides correctly. 3. Pick the ratio you need. 4. Substitute the lengths. 5. Simplify the fraction if needed.

Diagram support

Use one right triangle and label the same angle A. Mark opposite, adjacent, and hypotenuse clearly before writing the ratios.

How CBSE asks it

CBSE may ask for the value of a ratio from given side lengths, or ask which ratio matches a side arrangement in a triangle.

Avoid common mistakes

Common confusion

Students often write tan A as adjacent divided by opposite, but that is actually cot A.

Common wrong answer

A common wrong answer is to use the wrong side order in tangent. That gives the reciprocal ratio and changes the answer completely.

Exam tip

Remember the order with a short check: sine and cosine both use the hypotenuse, while tangent does not.

Quick check

If the opposite side is 7 cm and the adjacent side is 24 cm, which ratio gives tan A?

tan A is opposite divided by adjacent, so here tan A = 7/24. The hypotenuse is not used in tangent.

Answer writing and exam use

1-mark answer

Sin A, cos A, and tan A are the basic trigonometric ratios formed from the opposite, adjacent, and hypotenuse sides of a right triangle.

2-mark answer

Sin A, cos A, and tan A are the basic trigonometric ratios formed from the opposite, adjacent, and hypotenuse sides of a right triangle. sin A = opposite/hypotenuse, cos A = adjacent/hypotenuse, tan A = opposite/adjacent. If for angle A the opposite side is 4 cm, adjacent side is 3 cm, and hypotenuse is 5 cm, then sin A = 4/5, cos A = 3/5, and tan A = 4/3.

3-mark answer

These three ratios are the starting point of the chapter. Sine uses opposite over hypotenuse, cosine uses adjacent over hypotenuse, and tangent uses opposite over adjacent. If the sides are identified correctly, the ratio becomes simple and direct. sin A = opposite/hypotenuse, cos A = adjacent/hypotenuse, tan A = opposite/adjacent. For angle A, if opposite = 6 cm and adjacent = 8 cm, then tan A = 6/8 = 3/4 after simplification. CBSE may ask for the value of a ratio from given side lengths, or ask which ratio matches a side arrangement in a triangle. A common wrong answer is to use the wrong side order in tangent. That gives the reciprocal ratio and changes the answer completely.
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