Question

Suppose sin(A)=-0.78. use the trig identity sin^2(A)+cos^2(A)=1 and the trig identity tan(A) = sin(A)/cos(A) to find tan(A) in quadrant IV. round to the ten-thousandth.
a. -0.2039
b. 1.3941
c. 0.8671
d. -1.2464

Answer 1

In quadrant IV, $\cos(A)$ is positive. So

$\sin^2(A) + \cos^2(A) = 1 \implies \cos(A) = \sqrt{1-\sin^2(A)} \approx 0.6258$

Then by the definition of tangent,

$\tan(A) = \dfrac{\sin(A)}{\cos(A)} \approx \dfrac{-0.78}{0.6258} \approx \boxed{-1.2465}$