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JAMB Mathematics 2022 Paper

Question : 6

Total: 39

If sin θ = -

\frac{3}{5}

and θ lies in the third quadrant, find cos θ

Solution:

Concept:

Use the Pythagorean identity and the sign of cosine in the third quadrant.

Explanation:

Given

\sin \theta = -\frac{3}{5}

, so the opposite side has magnitude

3

and the hypotenuse has magnitude

5

Using Pythagoras:

\text{hypotenuse}^2 = \text{adjacent}^2 + \text{opposite}^2

5^2 = \text{adjacent}^2 + 3^2

This gives

\text{adjacent}^2 = 25 - 9 = 16

Therefore,

\text{adjacent} = 4

Thus,

\cos \theta = \frac{\text{adjacent}}{\text{hypotenuse}} = \frac{4}{5}

in magnitude.

Since

\theta

lies in the third quadrant, cosine is negative in that quadrant.

Hence,

\cos \theta = -\frac{4}{5}

Answer:

-\frac{4}{5}

(Option D).

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