if tanθ = 3/4, 180°

Correct Answer is : - 45\;4/554

Correct Answer is : - 45\;4/554

Test Index

WAEC Mathematics 2021 Paper

Question : 22

Total: 49

if tanθ =

\frac{3}{4}

, 180° < θ < 270°, find the value of cosθ.

Solution:

Concept:

Use the given tangent ratio to find the hypotenuse, then apply the sign of cosine in the third quadrant.

Explanation:

Given

\tan\theta = \frac{3}{4}

and

180^\circ < \theta < 270^\circ

, so

\theta

lies in the third quadrant.

Since

\tan\theta = \frac{\text{opposite}}{\text{adjacent}} = \frac{3}{4}

, take opposite

= 3

and adjacent

= 4

Hypotenuse

= \sqrt{3^2 + 4^2} = \sqrt{9 + 16} = \sqrt{25} = 5

Thus, the magnitude of cosine is

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

In the third quadrant, cosine is negative.

Therefore,

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

Answer:

-\frac{4}{5}

, which is option C.

Go to Question:

Prev Question

Next Question