# Math 1113 Final Exam Review

**Section 4**

For problems 1-3 you are given the rate of rotation of a wheel as well as its
radius.

In each case, determine the following:

a. the angular speed, in units of radians/sec.

b. the linear speed , in units of cm/sec, of a point on the circumference of the

wheel

1. 6 revolutions/sec; r = 12 cm ans: a. 12π rad/sec b. 144π

cm/sec

2. 1080° /sec; r = 25 cm ans: a. 6π rad/sec b. 150π

cm/sec

3. 500 rpm; r = 45 cm ans: a. rad/sec b. 750π

cm/sec

4. Find the values of the six trigonometric functions of the angle in

standard position with the terminal side passing through the point (1, −3).

ans:

5. If θ is an acute angle in standard position and sinθ = 3/5
, find secθ .

ans: 5/4

6. Find amplitude and period of the function

ans: amp = 4, period = 3/2

7. Determine an equation for a cosine curve that has amplitude of 3, period

of π, and phase shift of π/4 to the left.

ans:

8. Determine an equation for a sine curve that has amplitude of 2, period

of 2, and phase shift of 2/3
to the right.

ans

9. Given that sinθ > 0; find secθ
.

ans:

10. A tree casts a shadow of 8.55 ft when the angle of elevation of the sun

is 55.3°. Find the height of the tree.

ans: 12.3 feet

11. Find x- intercepts of each trigonometric function in the speciffied interval.

ans:

ans:

12. Find exact value of ans:

13. Find exact value of ans: 3/5

14. Find exact value of ans:

15. Find horizontal asymptote of [look this up in your notes]

**Section 5**

Verify the following identities (# 1 - 3).

1.

2. (sin x + cos x)(csc x − sec x) = cot x − tan x

3.

Simplify (# 4 - 6).

4. ans: − sin x

5.

ans: cos x

6.
α and
β are in quadrant II; find
.

ans:− 16/65

Verify each identity (#7 -8).

7.

8.

Find all solutions of each equation in the interval 0,2.

9. tan x − 2tanx cos x = 0

ans:

10. 2cos^{2}x − cos x = 1

ans:

11. 2sec^{3}x + sec^{2}x − 8secx − 4 = 0

ans:

Find all solutions of each equation in the interval

12. tan^{2}x = 3sec^{2}x − 2

ans: No solution

13. cos^{2}x − 3sinx + 2sin^{2}x = 0

ans: 22.5°, 157.5°

14. cos x + 3 = 0

ans: No solution

15.

ans: 30°,150°,240°,300°

**Section 6**

Solve each triangle (#1 - 5).

1. a = 24, b = 32, c = 28

ans:C ≈ 58° A ≈ 47° B = 76°

2. b = 102, c = 150, A = 82°

ans: a ≈ 169 B = 37° C = 61°

3. C = 55°, c = 80, b = 110

ans:No triangle is formed, as sinB ≈ 1.1263

4. B = 25°, C = 40°, c = 40

ans:A = 115° a ≈ 56 b ≈ 26

5. A = 37°, c = 40, a = 28

ans: C = 59°, B = 84°, b = 46 or C = 121°, B = 22°, b = 17

6. Find the components of a vector whose initial and terminal points are

.

ans:

7. Find the magnitude and direction of the vector

ans: magnitude = 10, direction = 120°

8. Find the magnitude and direction of z = 2 − 3i.

ans:

9. Write the complex number z = 5 (cos315° + i sin315°) in standard form.

ans: z ≈ 3.54 − 3.54i

10. Find the vertices and asymptotes of the hyperbola

ans: vertices – (0,2), (0, −2)

asymptotes

11. Find the vertices of the ellipse

ans: (−6,0), (6,0)

12. Find the 30th term of the sequence

ans: − 10/11

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