Question

Part A: Given sine of theta is equal to radical 3 over 2 comma determine three possible angles θ on the domain [0,∞). (5 points)Part B: Given θ = 675°, convert the value of θ to radians and find sec θ. (5 points)

Answer 1

Solution

Part A

For this case we can do the following:

$\sin \theta=\frac{\sqrt[]{3}}{2}$

We can solve for theta and we have:

$\theta=\sin ^{-1}(\frac{\sqrt[]{3}}{2})=\frac{\pi}{3}+2\pi n$

Then three possible angles are:

$\theta=\frac{\pi}{3},\frac{7\pi}{3},\frac{13\pi}{3}$

Part B

We have the following angle theta= 675º

And we want to find the value in radians and the find the secant so we can do this:

$\frac{\pi}{180}=\frac{x}{675}$

Solving for x we got:

$x=\frac{15}{4}\pi$

And then we can find the secant and we have:

$\sec (\frac{15\pi}{4})=\sqrt[]{2}$