Free Printable Segment 2 Exam Part 1

1.

Determine a co-terminal angle of 1215°.

a)

2π/3

b)

3π/2

c)

3π/4

d)

4π/3

2.

Given triangle ABC, if A=62°, B=66°, and b=10, find side c.

a)

8.6

b)

9.4

c)

8.1

d)

7.8

3.

Given triangle ABC, if the distance from A to B is 400, B to C is 600, and C to A is 800, what is the smallest angle?

a)

46.56°

b)

104.48°

c)

26.91°

d)

28.96°

4.

What is the area of a regular octagon inscribed in a circle of radius 5 ft?

a)

14.1421 square feet

b)

70.7107 square feet

c)

8.8388 square feet

d)

35.3554 square feet

5.

At which angle is csc(𝞡) = √2?

a)

5𝝅/4

b)

3𝝅/4

c)

7𝝅/6

d)

7𝝅/4

6.

Given: cot θ = 1, and 180° ≤ θ ≤ 270°, what is sec θ = ?

a)

$-\ \sqrt[]{2}$

b)

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

c)

$\sqrt[]{2}$

d)

1

7.

The path that a roller coaster takes can be modeled by the function

R(t)=15sin2t+30, where t represents the time in

seconds and R is the height of the coaster. Based on the graph, at what time will the roller coaster reach the maximum height for the first time?

a)

3𝝅/4

b)

𝝅

c)

𝝅/4

d)

5𝝅/4

8.

Graph the function: f(x)=csc(1/2(x-𝝅))-2. What is the period?

a)

2𝝅/3

b)

𝝅/2

c)

3𝝅

d)

4𝝅

9.

Graph the function: f(x)=1/2 tan(4(x+𝝅/8). Identify the period and phase shift.

a)

4𝝅; 𝝅/8

b)

𝝅/4; -𝝅/8

c)

𝝅/4; 𝝅/8

d)

4𝝅; -𝝅/8

10.

The average monthly temperature M(t), in degrees Fahrenheit, of a particular city in Alaska can be modeled by the sinusoidal function M(t)=15sin(t𝝅/6+𝝅/6), where t=1 represents January. Algebraically determine the months in which the average monthly temperature equals 0°F.

a)

June and December

b)

April and November

c)

May and November

d)

May and December

11.

Given v= < -9, 4>, what are the magnitude and direction of v? Round the magnitude to the thousandths place and the direction to the nearest degree.

a)

9.849; -24°

b)

8.062; 156°

c)

9.849; 156°

d)

8.062; -24°

12.

Which of the following identities is equal to $1+\tan^2θ$ ?

a)

$\sec^2θ$

b)

$\csc^2θ$

c)

$\cot^2θ$

d)

$\sin^2θ$

13.

Which of the following shows the simplified function of

$\frac{\cos^2x}{1-\sin x}$ ?

a)

1 + cos x

b)

1 − cos x

c)

sin x+1

d)

sin x-1

14.

What is the exact value of $\cos\left(\frac{29\pi}{12}\right)$ ?

a)

$\frac{\sqrt[]{6}+\ \sqrt[]{2}}{4}$

b)

$\frac{\sqrt[]{6}-\ \sqrt[]{2}}{4}$

c)

$\frac{\sqrt[]{2}-\ \sqrt[]{6}}{4}$

d)

$\frac{-\sqrt[]{2}-\ \sqrt[]{6}}{4}$

15.

What are the solutions to the equation $\sin\left(x-\pi\right)\ =\ \frac{\sqrt[]{3}}{2}$ on the interval [0, 2π)?

a)

$\left(\frac{\pi}{3}\ ,\ \frac{2\pi}{3}\right)$

b)

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

c)

$\left(\frac{5\pi}{6}\ ,\ \frac{11\pi}{6}\right)$

d)

$\left(\frac{4\pi}{3}\ ,\ \frac{5\pi}{3}\right)$

16.

What are all of the solutions to the trigonometric equation $2\cos^2\theta\ -\ 2\sin^2\theta\ =\ 1$ ?

a)

$\theta\ =\ \frac{\pi}{3}\ +\ \pi n\$ and $\theta\ =\ \frac{5\pi}{3}\ +\ \pi n$

b)

$\theta\ =\ \frac{\pi}{3}\ +\ 2\pi n$ and $\theta\ =\ \frac{5\pi}{3}\ +\ 2\pi n$

c)

$\theta\ =\ \frac{\pi}{6}\ +\ \pi n\$ and $\theta\ =\ \frac{5\pi}{6}\ +\ \pi n$

d)

$\theta\ =\ \frac{\pi}{6}\ +\ 2\pi n$ and $\theta\ =\ \frac{5\pi}{6}\ +\ 2\pi n$

17.

The expression (tan θ)(cos θ)(cot θ) simplifies to which of the following?

a)

cos θ

b)

sin θ

c)

cot θ

d)

1

18.

Determine all solutions to the equation $-\ \sqrt[]{2}\ \cos2x\ =\ \sin^2x\ +\ \cos^2x$ on the interval [0, 2π).

a)

$x\ =\frac{3\pi}{4},\ \frac{5\pi}{4}$

b)

$x\ =\frac{3\pi}{4},\ \frac{5\pi}{4},\ \frac{11\pi}{4},\ \frac{13\pi}{4}$

c)

$x\ =\frac{3\pi}{8},\ \frac{5\pi}{8},\ \frac{11\pi}{8},\ \frac{13\pi}{8}$

d)

$x\ =\frac{3\pi}{8},\ \frac{5\pi}{8}$

19.

Based on the graph of the trigonometric functions f (θ) = 2sin θ - 2 and g (θ) = cos 2θ, at what value(s) on the interval [0, 2π) does f (θ) = g (θ)?

a)

0, π

b)

π/2 , π

c)

π/3, π

d)

π/3, 2π/3

20.

Mullet fish are known to jump out of the water when being pursued by predators. The height in inches of one mullet fish can be described by the function $f\left(x\right)\ =\ 2\cos^2x-1$ , where x represents the time in seconds. Another mullet fish's height from the water level can be represented by the equation g(x) = sin x. At which values on the interval [0, 2π) will the two fish be at the same height above the water?

a)

π/6

b)

0, π

c)

π/6, 5π/6

d)

π/6, 5π/6, 3π/2

Segment 2 Exam Part 1

Total questions: 20

Worksheet time: 5hrs 0mins

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