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

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})=(\pi)/(3)+2\pi n`

Then three possible angles are:

`\theta=(\pi)/(3),(7\pi)/(3),(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:

`(\pi)/(180)=(x)/(675)`

Solving for x we got:

`x=(15)/(4)\pi`

And then we can find the secant and we have:

`\sec ((15\pi)/(4))=\sqrt[]{2}`