Question

If sin theta = 4/5 and cos theta is in quadrant II, then cos theta and tan theta equal what?​

Answer 1

Answer:

In quadrant ll,

cos theta = -3/5

tan theta = -4/3

Step-by-step explanation:

In quadrant ll, only sin is positive, cos and tan are negative

sin theta = opposite/hypotenuse = 4/5

From Pythagoras theorem,

adjacent = sqrt(hyp^2 - opp^2) = sqrt(5^2 - 4^2) = sqrt(25 - 16) = sqrt(9) = 3

cos theta = adjacent/hypotenuse = -3/5

tan theta = opposite/adjacent = -4/3

Answer 2

Using the pythagorean identity, $\cos^2{\theta} + \sin^2{\theta} = 1$. Since $\theta$ is in quadrant ||, we know that $\cos{\theta}$ is negative. Solving the equation $\cos^2{\theta} + (\frac{4}{5})^2 = 1$ for $\cos{\theta}$, we get that $\cos{\theta} = -\frac{3}{5}$.

$\tan{\theta}$ is equal to $\frac{\sin{\theta}}{\cos{\theta}}$, which is $-\frac{4}{3}$.