Reference Angles and Trig Equations

Reference Angles Review

Key Points for Reference Angles

• Acute Angle between the x axis and the terminal side of the angle

• Always Positive

• Never between y-axis and terminal side

Multiple Select

Which if the following have a reference angles of 50⁰? Select all that apply.

• 130^o

• 230^o

• 150^o

• 310^o

• 350^o

Multiple Choice

For which of the following is 30 degrees NOT a reference angle for ?

• $$\frac{10\pi}{12}$$  

• $$\frac{11\pi}{6}$$  

• 240 degrees

• 210 degrees

Multiple Choice

When does  $$\sin\left(\theta\right)=-\frac{1}{2}$$  

• $$\theta=\frac{5\pi}{6\ }\ or\ \frac{7\pi}{6\ }$$  

• $$\theta=\frac{5\pi}{6\ }\ or\ \frac{11\pi}{6}$$  

• $$\theta=\frac{7\pi}{6\ }\ or\ \frac{11\pi}{6}$$  

Multiple Choice

When does  $$\cos\left(\theta\right)=-\frac{1}{2}$$  

• $$\theta=\frac{2\pi}{3\ }or\frac{5\pi}{3\ }$$  

• $$\theta=\frac{2\pi}{3\ }or\frac{4\pi}{3\ }$$  

• $$\theta=\frac{4\pi}{3\ }or\ \frac{5\pi}{3\ }$$  

Multiple Choice

When ix tan(x) =undefined?

• $$x=\ 0\ or\ 180$$  

• $$x=\frac{\pi}{2\ }or\ \frac{3\pi}{2}$$  

• $$\frac{\pi}{4}\ and\ \frac{3\pi}{4}$$  

• Your face is undefined

Multiple Select

When does  $$\sin\left(\theta\right)=0$$  ? Select all that apply

• $$\theta=0\ \ or\ \pi$$  

• $$\theta=\frac{\pi}{2\ }\ or\ \frac{3\pi}{2}$$  

• $$\theta=\frac{\pi}{2\ }\ or\ 2\pi$$  

• $$\theta=2\pi\ or\ 7\pi$$  

Multiple Select

Which of the following have the same reference angle? Select all that apply.

• $$105\degree$$  

• $$435\degree$$  

• $$205\degree$$  

• $$285\degree$$  

Multiple Select

Within which quadrants is sin(x) = negative?

• I

• II

• III

• IV

Multiple Select

W ithin which quadrants is If cos(x) = positive?

• I

• II

• III

• IV

Multiple Select

If sin(x) = a value between -1 and 1, there are aloways two values for x

• sometimes

• always

• never

Multiple Select

Which option(s) below have zero solution between 0 and 360 degrees

• sin(x) = -3/4

• sec(x) = 2

• sec(x) = 1/2

• sin(x) = 1

• cos(x) = - 2