Download Math 1316--Final Exam Review

Math 1316 Review for Final Exam
Final Exam is Tuesday, May 12, 2015, 9:00 – 11:00 a.m.
You will need a calculator with trig functions (NOT a graphing calculator) for this test.
I will provide the trig identities and the formulas from chapters 3 and 4 for you to use.
You may prepare one page of notes to use on the test (8 ½” x 11”, front & back OK).
In addition to this review sheet, you should study old reviews, tests, and homework.
1. For θ = 785o, draw θ in standard position, give two angles which are coterminal with θ and give
the reference angle, θ’.
2. Given the right triangle with adjacent side = 15 and hypotenuse = 17, find sin α, cos α, and tan α.
3. If (-3, -4) is a point on the terminal side of angle φ in standard position, draw φ and use the x-y-r
definitions to find sin φ and tan φ.
4. Give the exact value of each. Values from calculators will not be accepted.
b) sin 180o c) tan( −3π / 4)
d) sec 135o e) cot 330o
a) csc(7π / 4)
f) sin[tan-1 (-12/5)]
5. Describe all of the transformations from the basic graph for each of the given functions:
1
2
π
a. y =
− sec( x − ) − 3
b. y 4 tan(2 x +
=
4
π
3
)
π
=
y 3 sin( x − )
6. Graph at least one period of:
4
15
sin A =
17
7.
Given:
8.
Given: cos A = −
2
5
and A is in QII ; tan B =
and A is in QIII.
5
12
and B is in QIII.
Find: cos(A – B)
Find: cos 2A
9. Verify the identity: cos x cos 2x = cos x – sin 2x sin x
10. Solve the equation. Give all answers in the first revolution. You may give either radians or
degrees: 2 sec 2x – 1 = 4 sec 2x + 3
11-12 Answer the requested question regarding each triangle.
11. a = 15; b = 27; c = 38 ; Find B.
12.
A = 52O; a = 83, B = 12O ; Find b.
13. An observer in a lighthouse is 66 m above the surface of the water. He sees a ship at an angle
of depression of 40O. How far is the ship from the base of the lighthouse?
14 - 16 Let v = 4,7
and w = −1,2
14. Find 2v + 6w
15. Find the direction angle for w.
16. Find the magnitude of v, the magnitude of w, and the dot product of v and w. Use these to
calculate the angle between v and w.
17. Plot the complex numbers on a complex plane (Label with letter):
b) -2i
c) 3 cis 180o
d) 2 2 cis 315o
a) −1 + i 3
18. Change the complex number from trig form into standard form: 5 cis 210O.
19. Change the complex number from standard form to trig form: 4 3 − 4i .
20. Multiply in trig form, then give answer in standard form: (3 cis 230o).(2 cis 250o)
21. Divide in trig form, then give answer in standard form: (8 cis 120o) / (4 cis 30o)
22. Raise to the power using DeMoivre's Theorem; give answer in standard form: (3 cis 315o)4.
23. Find the three cube roots of 8i . Give answers in standard form.
24. Convert: a) (4, π) from polar into rectangular.
b) (3 3, 3) from rectangular into polar.
--------------------------------------------------------------------------------------------------------------------------------Answers:
1.
3.
coterminal: 425o , 65o, ref angle: 65o
sin α = 8/17, cos α = 15/17, tan α = 8/15
sin φ = -4/5, tan φ = 4/3
a) − 2 b) 0 c) 1 d) − 2 e) − 3
f) -12/13
a) vertical reflection; vertical shrink by ½; hor. trans. to right π/4; vertical trans. down 3
b) vertical stretch by 4; new period = π/2; horizontal trans. to left π/6.
6. graph ----->
7. 21/221
8. -17/25
3
9. proof
10. {60o, 120o, 240o, 300o}
11. 34.46o
12. 21.90
π/4
5π/4
7π/4
11π/4
13. 78.66 m
14. <2, 26>
-3
o
15. 116.57
16. 65, 5, 10 , 56.31o
17. graph ----->
1.
2.
3.
4.
5.
18. −
19.
20.
21.
22.
23.
5 3 5
− i
2
2
2
8 cis 330o
−3 + 3 3i
2i
-81
3 + i , − 3 + i , − 2i
{
24. a) (-4, 0)
(a) 1
-3 -2 -1
(c)
}
b) (6, π/6) or (-6, 7π/6)
0
-1
-2 (b)
1
2
(d)
3