Algebra 2 Trigonometry

Review how to solve trig equations

​Have your unit circle ready and you may want to have Desmos open as well.

Multiple Choice

Solve on the domain [0,2π)
cos x + 1 = 0

• 0
• No solution
• π
• 3π/2

Multiple Choice

Which of these is NOT
 a solution to
tan θ = 0 ?

• θ = 0
• θ = π /2
• θ = π
• θ = 2π

Multiple Choice

Solve on the Interval [0,2π) 
   sinθ = -1   

• θ = π /2, 3π /2 
• θ = π /2
• θ = 3π /2
• θ = π  

Multiple Select

Solve the equation for $$0\degree\le\theta\le360\degree$$ . Select ALL correct answers.

$$\tan\theta=-\sqrt{3}$$  

• $$60\degree$$  

• $$120\degree$$  

• $$240\degree$$  

• $$300\degree$$  

Multiple Select

Solve the equation for $$0\degree\le\theta\le360\degree$$ . Select ALL correct answers.

$$6\sin\theta=3$$  

• $$60\degree$$  

• $$300\degree$$  

• $$30\degree$$  

• $$150\degree$$  

Multiple Select

Solve the equation for $$0\degree\le\theta\le360\degree$$ . Select ALL correct answers.

$$4\cos\theta=-2$$  

• $$60\degree$$  

• $$120\degree$$  

• $$240\degree$$  

• $$300\degree$$  

Multiple Choice

Solve equation for $$0\le\theta<2\pi$$  .
$$6\tan\theta\ +\ 6\sqrt{3}\ =\ 0$$  

• $$\theta=\frac{\pi}{6},\frac{7\pi}{6}$$  

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

• $$\theta=\frac{\pi}{3},\frac{4\pi}{3}$$  

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

Multiple Select

Solve the equation for $$0\degree\le\theta\le360\degree$$ . Select ALL correct answers.

$$5+\tan\theta=4$$  

• $$45\degree$$  

• $$135\degree$$  

• $$225\degree$$  

• $$315\degree$$  

Multiple Select

Solve the equation for $$0\degree\le\theta\le360\degree$$ . Select ALL correct answers.

$$-15+4\cos\theta=-15-2\sqrt{2}$$  

• $$45\degree$$  

• $$135\degree$$  

• $$225\degree$$  

• $$315\degree$$  

Multiple Choice

$$Solve\ \ 2\sin^2x\ +\ \sin x\ -\ 1\ =\ 0\ \ for\ 0\ \le\ x\ <\ 360$$  

• $$30\degree,\ 90\degree,\ 150\degree$$  

• $$90\degree,\ 210\degree,\ 330\degree$$  

• $$30\degree,\ 150\degree,\ 270\degree$$  

• $$210\degree,\ 270\degree,\ 330\degree$$  

Multiple Choice

Solve on the Interval [0,2π)
tan(x)+1=2

• 0 and π  
• 3π/4 and 7π/4
• π/4 and 5π/4
• 3π/4 and 5π/4

Let's look at the Unit Circle

Multiple Choice

Based on the unit circle, what is the value of sin?

• y

• x

• x/y

• y/x

Multiple Choice

Based on the unit circle, what is the value of cos?

• y

• x

• x/y

• y/x

Multiple Choice

Based on the unit circle, what is the value of tan?

• y/r
• x/r
• r/y
• y/x

Dropdown

Find the exact value of the following trig expressions.



Try to remember these results without looking at the unit circle.



$$\sin\left(\frac{\pi}{3}\right)=$$ ​

Select answer

$$\sin\left(\frac{7\pi}{6}\right)=$$ ​ ​ ​

Select answer

$$\cos\left(\frac{5\pi}{4}\right)=$$ ​

Select answer

$$\cos\left(-\frac{\pi}{3}\right)=$$ ​

Select answer

Multiple Choice

$$\frac{2\pi}{3}$$  lies in which quadrant?

• QI

• QII

• QIII

• QIV

Multiple Choice

Convert π radians to degrees.

• 90⁰
• 180⁰
• 360⁰
• 60⁰

Multiple Choice

A full rotation is _____ radians.

• $$\frac{\pi}{2}$$

• $$\pi$$

• $$2\pi$$

• $$4\pi$$

Multiple Choice

What is the exact coordinates of  3π/4 on the unit circle?

• (−√2∕2, √2∕2)
• (−√2∕2, −√2∕2)
• (−√3∕2, −√2∕2)
• (√2∕2, −√2∕2)

Multiple Choice

tan 7π/4

• -1
• 1
• √2/2
• undefined

Multiple Choice

tan(300^o)

• -√3 /3
• ½
• 2√3 /3
• -√3

Multiple Choice

sec 3π/2

• 0
• undefined
• 1
• -1

Multiple Choice

tan(3π/4)

• √2/2
• -√2/2
• √3/2
• -1

Poll

After this review, I feel --- about the Unit Circle AND how to solve basic trig equations

• very good/ very confident

• good/confident

• eh...so-so; I'm iffy about how to solve the equations

• lost; dazed and confused about the whole matter

• other: my thoughts/feelings are not listed here