Free Printable Summative Review (AA 3.4-3.6)

1.

Convert 40 degrees to radians.

a)

$\frac{\pi}{9}$

b)

$\frac{2\pi}{9}$

c)

$\pi$

d)

$\frac{\pi}{90}$

2.

Convert $\frac{3\pi}{4}$ to degrees.

(a)

3.

When angle $\theta$ is given in radians, what is the formula for length of an arc for a circle?

a)

$l\ =\ \frac{1}{2}r^2\theta$

b)

$l\ =\ \frac{r}{\theta}$

c)

$l\ =\ r\theta$

d)

$l\ =\ r^2\theta$

4.

A circle with radius 5 cm has an arc which subtends an angle of 60 degrees. Find the length of the arc in radians.

a)

$\frac{5\pi}{3}$

b)

300

c)

$\frac{25\pi}{3}$

d)

5 cm

5.

A circle with a radius of 5 cm has an arc length 8 cm which subtends an angle $\theta$ . Find the size of $\theta$ in radians to 2 significant figures.

(a)

6.

What is the formula for area of a sector?

a)

$A\ =\ r\theta$

b)

$A\ =\ r^2\theta$

c)

$A\ =\ \frac{1}{2}r\theta$

d)

$A\ =\ \frac{1}{2}r^2\theta$

7.

The radius of a circle is 5 cm. Find the area of a sector of the circle with a central angle of 1.3 radians. Type your answer with 4 significant figures and no units.

(a)

8.

Which saying goes with the Unit Circle to help you determine which trig function is positive and negative?

a)

Team Astros Terrorize Cubs

b)

Students Also Take Calculus

c)

All Students Take Calculus

d)

Cake Taste So Good

9.

In quadrant 3 of the unit circle, which trig function is positive?

a)

cos

b)

sin

c)

tan

d)

all

10.

$\cos\left(\pi-x\right),\ 0\ <\ x\ <\ \frac{\pi}{2}$

Which quadrant is this in?

a)

1

b)

2

c)

3

d)

4

11.

$\sin\left(3\pi+x\right),\ 0\ <\ x\ <\ \frac{\pi}{2}$
Is this positive or negative?

a)

Positive

b)

Negative

12.

What is the reference angle (in degrees) of $\frac{5\pi}{4}$ ?

a)

30 degrees

b)

45 degrees

c)

60 degrees

d)

90 degrees

13.

What is the exact value of $\sin\left(\frac{\pi}{3}\right)$ ?

a)

0.866

b)

$\frac{\sqrt{3}}{2}$

c)

$\frac{1}{2}$

d)

$\frac{\sqrt{2}}{2}$

14.

What is the exact value of $\cos\left(\frac{3\pi}{4}\right)$ ?

a)

-1.41

b)

-0.707

c)

$\frac{-\sqrt{2}}{2}$

d)

$\frac{-\sqrt{3}}{2}$

15.

$\tan\left(\frac{11\pi}{6}\right)$

What is the exact value of

a)

$\sqrt{3}$

b)

$-\sqrt{3}$

c)

$\frac{\sqrt{3}}{3}$

d)

$\frac{-\sqrt{3}}{3}$

16.

Triangle ABC has angle B = 40 degrees and side lengths b = 8 cm and c = 11 cm. How would you find the two possible measures of angle C?

a)

Use the cosine rule to find angle C, which will be your possible acute angle for C. Then you do 180 minus what you got and that is the second possible angle.

b)

Use the sine rule to find angle C, which will be your possible acute angle for C. Then you do 180 plus what you got and that is the second possible angle.

c)

Use the sine rule to find angle C, which will be your possible acute angle for C. Then you do 180 minus what you got and that is the second possible angle.

d)

Use the cosine rule to find angle C, which will be your possible acute angle for C. Then you do 180 plus what you got and that is the second possible angle.

17.

What is the pythagorean identity?

a)

$\cos^2\theta\ +\ \sin^2\theta\ =\ 1$

b)

$\cos\theta\ +\ \sin\theta\ =\ 1$

c)

$a^2\ +\ b^2\ =\ c^2$

d)

$\cos^2\theta\ -\ \sin^2\theta\ =\ 1$

18.

Find the possible exact values of $\sin\theta$ for $\cos\theta=\frac{4}{5}$ for $\pi\ <\ \theta\ <\ \frac{3\pi}{2}$ .

a)

-3/5

b)

3/5

c)

4/5

d)

-2/5

19.

Which identity does not equal to $\cos2\theta$ ?

a)

$\cos^2\theta-\sin^2\theta$

b)

$2\cos^2\theta-1$

c)

$1-2\sin^2\theta$

d)

$2\sin\theta\cos\theta$

20.

If $\sin2\theta\ =\ \frac{\sqrt{3}}{2}$ and $\cos2\theta\ =\ \frac{1}{2}$ , find the exact value of $\tan2\theta$ .

a)

1.73

b)

$\sqrt{3}$

c)

$\frac{\sqrt{3}}{3}$

d)

0.577

e)

$\frac{\sqrt{3}}{4}$

Summative Review (AA 3.4-3.6)

Total questions: 20

Worksheet time: 25mins

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