Algebra 2 Unit 5: Trigonometric Functions

Radians, the unit circle, amplitude, period and midline, the Pythagorean identity and simple trig equations. 12 questions. Have a go at each one on paper before you tap "Show me how".

A free account opens the worked solutions to 20 questions a day; Pro opens every one.

Question 1

Radian measureNo calculator

What is $\frac{5\pi}{6}$ radians in degrees?

1. $120$
2. $300$
3. $150$
4. $165$

Question 2

The unit circleNo calculator

Using the unit circle, give the exact value of $\sin\frac{7\pi}{6}$.

1. $\frac{\sqrt{3}}{2}$
2. $-\frac{\sqrt{3}}{2}$
3. $-\frac{1}{2}$
4. $\frac{1}{2}$

Question 3

The unit circleNo calculator

Without a calculator, find $\tan\frac{3\pi}{4}$ exactly.

1. $-1$
2. $1$
3. $\sqrt{3}$
4. $-\frac{\sqrt{3}}{3}$

Question 4

Amplitude and periodNo calculator

What are the amplitude and period of $y=3\sin(2x)-1$?

1. Amplitude $2$, period $3\pi$
2. Amplitude $3$, period $4\pi$
3. Amplitude $3$, period $\pi$
4. Amplitude $-1$, period $2\pi$

Question 5

MidlineNo calculator

What is the midline of $y=-2\cos x+5$?

1. $y=7$
2. $y=3$
3. $y=5$
4. $y=-2$

Question 6

Pythagorean identityNo calculator

Angle $\theta$ lies in Quadrant II and $\sin\theta=\frac{3}{5}$. Use the Pythagorean identity to find $\cos\theta$.

1. $\frac{5}{4}$
2. $-\frac{4}{5}$
3. $\frac{4}{5}$
4. $-\frac{3}{4}$

Question 7

Radian measureNo calculator

In which quadrant does an angle of 4 radians, in standard position, end?

1. Quadrant IV
2. Quadrant I
3. Quadrant III
4. Quadrant II

Question 8

PeriodNo calculator

What is the period of $y=\tan\frac{x}{2}$?

1. $\frac{\pi}{2}$
2. $4\pi$
3. $\pi$
4. $2\pi$

Question 9

Trigonometric equationsNo calculator

Solve $\sin x=\frac{\sqrt{3}}{2}$ for $0\le x<2\pi$.

1. $x=\frac{\pi}{3}$
2. $x=\frac{\pi}{3} \text{ or } x=\frac{4\pi}{3}$
3. $x=\frac{\pi}{6} \text{ or } x=\frac{5\pi}{6}$
4. $x=\frac{\pi}{3} \text{ or } x=\frac{2\pi}{3}$

Question 10

Trigonometric modelsNo calculator

A seat on a Ferris wheel is $h(t)=40-35\cos\left(\frac{\pi t}{4}\right)$ feet above the ground after $t$ minutes. What is its greatest height, in feet?

1. $75$
2. $5$
3. $40$
4. $35$

Question 11

The unit circleNo calculator

What point on the unit circle matches the angle $\frac{5\pi}{3}$?

1. $\left(\frac{1}{2},-\frac{\sqrt{3}}{2}\right)$
2. $\left(\frac{\sqrt{3}}{2},-\frac{1}{2}\right)$
3. $\left(-\frac{1}{2},\frac{\sqrt{3}}{2}\right)$
4. $\left(\frac{1}{2},\frac{\sqrt{3}}{2}\right)$

Question 12

Evaluating trig functionsCalculator

Find $\cos 2.5$, where 2.5 is in radians, to the nearest hundredth.

1. $0.80$
2. $1.00$
3. $-0.60$
4. $-0.80$