Find $\sec\theta$ and $\tan\theta$ if $\sin\theta = -3/4$ and in Quadrant 4. What am I doing wrong?

Question

I keep getting this flagged as wrong, but I'm not sure why

Find $\sec\theta$ and $\tan\theta$ if $\sin\theta = -3/4$ and in Quadrant 4.

My result was:

$\sec\theta = -4\sqrt7/7$

$\tan\theta = 3\sqrt7/7$

What am I missing?

Answer 1

I think you need to check the signs of your answers. The question states that the angle is in quadrant 4. Which trig functions are positive in quadrant 4 and which are negative?

Answer 2

Since $sin\theta=\frac{–3}{5}$ it must lie in third quadrant or fourth quadrant and we know that $tan\theta=\frac{sin\theta}{cos\theta}$ and $sin\theta=\frac{perpendicular }{hypotenuse}$therefore $hypotenuse =5$ and $perpendicular =3$ and $base=4$ therefore $tan\theta=±\frac{3}{4}$ and $sec\theta=±\frac{5}{4}$tan will be positive in third quadrant and sec will be positive in fourth quadrant.