Applying and analysing trigonometric functions

What is cos^-1(½)?

• ¼π, 45⁰
• ⅓π, 60⁰
• ½π, 90⁰
• π, 180⁰

Solve

sin²θ = ½

on θ∈[0, 2π)

• θ = π /4, 7π /4

• θ = π /4, 3π /4

• θ = 3π /4, 5π /4

• θ = π /4, 3π /4, 5π /4, 7π /4

Find all values of

 $\Theta$  , if  $\Theta$  is in the interval  $\left[0,360\degree\right)$  and has the given function value.

 $\sin\ \Theta=-\frac{1}{2}$  

•  $60\degree\ and\ 300\degree$  

•  $210\degree\ and\ 330\degree$  

•  $60\degree\ and\ 120\degree$  

•  $150\degree\ and\ 210\degree$  

Solve the trigonometric equation in the interval  $\left(0,\ 2\pi\right]$ .

 $2\sin3x+\sqrt{3}=0$  

•  $\frac{\pi}{2},\frac{2\pi}{3}$  

•  $\frac{4\pi}{3},\frac{5\pi}{3}$  

•  $\frac{4\pi}{9},\frac{5\pi}{9}$  

•  $\frac{\pi}{6},\frac{4\pi}{9},\frac{2\pi}{9},\frac{5\pi}{9}$  

Solve for x. Round to the nearest tenth.

• 103.5
• 4.7
• 55.0
• 23.4

Find the exact value of the expression below:

 $\sin^{-1}\left(\frac{\sqrt{3}}{2}\right)$  

•  $\frac{\pi}{3}$  

•  $-\frac{\pi}{2}$  

•  $-\frac{\pi}{3}$  

•  $-\frac{\pi}{6}$  

• 0.864

• 0.865

• 0.866

• 0.863

Answer explanation

Make sure your calculator is in the radians mode.

cos^-1(tan(-π/4))

• 0
• π
• π/4
• 3π/4

What is the value of tan⁻¹(−0.4) to two decimal places?

• −0.38

• −0.42

• −0.39

• −0.35