medium difficulty5 min

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.

In one line: Sine and cosine keep the hypotenuse in the denominator; tangent stays in the triangle.

Practice This Concept

Understand it

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.

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.

Formula and rule

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

See it worked out

Follow the example line by line, then use the same method on new questions.

Worked example

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

Method you can reuse

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

Sketch it in your answer

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

Check yourself

Answer the question in your head before opening the answer.

Try it yourself

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

Think first, then show answer

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

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.

Don't mix this up

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

Exam tip

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

Write it in the exam

Each point is worth about one mark. Write point 1 for a 1-mark question and keep adding points as the marks go up.

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.

1
Enough for 1 mark
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
Add for 2 marks
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.
3
Add for 3 marks
These three ratios are the starting point of the chapter.

MCQ Quiz

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