Question

If sin theta =4/5 and theta is in quadrant 2, the value of tan theta is?

Answer 1

Since

$\tan\theta=\dfrac{\sin\theta}{\cos\theta}$

and $\theta$ is in quadrant 2, we know $\cos\theta<0$, so $\tan\theta<0$ as well.

From the Pythagorean identity we have

$\cos^2\theta=1-\sin^2\theta\implies\cos\theta=-\sqrt{1-\left(\dfrac45\right)^2}=-\dfrac35$

Then

$\tan\theta=\dfrac{\frac45}{-\frac35}=-\dfrac43$

Answer 2

The value of tan theta is 4/3

Quadrant angles

Given the following parameters

• sin theta = 4/5

Get the adjacent side:

adj^2 = 5^2 - 4^2

adj^2 = 25 - 16

adj = √9

adj = 3

Get the measure of tan theta

tan theta = opposite /adjacent

tan theta = 4/3

Hence the value of tan theta is 4/3

Learn more on trigonometry here: https://brainly.com/question/20519838