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Exam Review Trig portion
Name
______________________
1.
What is the reference angle for 300 degrees
2.
What is the reference angle for -12 degrees
3.
What is the reference angle?
4.
What is the quadrant of the terminating side for 215 degrees
5.
What is the exact value of sin(
6.
7.
8.
9.
10.
11.
12.
What is the exact value of tan(60 degrees)?
What is the exact value of cos(420 degrees)?
Sin( 104 degrees)
Csc (19 degrees)
Cot (45 degrees)
Change 300 degrees to radians
Change 235 degrees to radians
8π
9
π
3
)?
13. The point (3, 4) is on the terminating side of an angle x, what is tan x ?
14. If the point (5, -12) is on the terminating side of an angle x, what is sin x ?
15. Analyze the sinusoidal equation Find equation for midline, amplitude, range
y = 7 sin( x ) + 10
16. Analyze the sinusoidal equation Find equation for midline, amplitude, range, phase shift
y = 3 sin(. x − π )
17. Analyze the sinusoidal equation Find equation for midline, amplitude, range, phase shift
18. What 2 quadrants are positive for sine?
Cosine?
y = −4 sin(θ − 6) + 7
Tangent?
19. The parent function of cosine crosses the y-axis at ____ (like a mountain)
Is it an even or odd function?
What is the symmetry?
20. Which of the following would be impossible because it violates the range of the parent function? Circle all that apply
a) sin x = 1.8
b) cos x = -7.3
c) sin x=-.8
d) sec x = 1.8
21.
cot 2 x sec 2 x
22.
About how many radians are in a straight line (180 degrees)?
Exactly how many?
23. About how many radians are in one complete rotation? Exactly how many?
24. About how many degrees are in one radian?
25. What is the radius of the unit circle?
26. Find the height of a tree given the length of its shadow is 150 feet. The angle of elevation from the ground is 52 degrees.
27. The inverse trig functions are also known as _____.
3
find cotθ
cosθ
7
29. Find the exact value of tan 45 + sin 90 + cos180
28. Given
30.
tan θ =
(1+ tan x )cos
2
2
x
31. In a right triangle, the side opposite angle θ measures 40 cm. The hypotenuse measures 41 cm.
Find the measure of angle θ and the tan θ .
tan 2 x cos 2 x
32.
θ
33. Identify all parts including both ways tangent is represented
34. The range of the parent sine function is
cosine function is
tangent function is
35. A hawk spies a snake on the ground. The angle of depression is 53 degrees from the Hawk to the snake. (So the angle of
elevation from the snake to the hawk is also 53 degrees!) The hawk flies at an elevation of 158 feet. If the hawk flies a
diagonal directly to the snake, how long is that hypotenuse pat
path?
36. A ________________ angle separates the quadrants
quadrants.
37. Two ________________ angles share the same terminating side.
38. Reference angles are always _____________ and measured to the ____ axis
axis.
39. When reciprocals multiply each other they cancel out and lleave _____.
40. The original midline for all parent trig functions is the horizontal line _______
41. Rewrite the sine function using its reciprocal function. sin (x) =
tan x =
2
, find csc x.
3
52.
If
53.
Given
54.
What is the period for the parent sine function?
55.
What is the exact value of cosine
ne (30 degrees)? (Use your unit circle!)
56.
Use identities to rewrite 2 different ways
58.
When looking for an angle given the lengths of the opposite side and the hypotenuse, use this function
f = 9 and d = 13, find the measure of angle E. Refer to the diagram on the right.
tan(x) =
59. Simplify each trig expression
cosθ secθ + tan 2 θ
1
1
+
2
sec θ csc 2 θ
cos 2 θ − 1
sin 2 θ − 1
(cos2 θ + sin 2 θ ) + cot 2 θ
sec x cot x
sin θ tan θ cscθ cot θ cosθ
cos2 x + sin 2 x
tan 2 x
rd
st
62.
A baseball diamond is actually a square with each side 90 feet in length. The direct distance from 3 base to 1 base is the
rd
st
diagonal of the square. Using your knowledge of special triangles, list the exact distance of the diagonal from 3 base to 1 base.
63.
Find the distance from the plane to point G.
64. Find two angles, one positive and one negative, that are coterminal with the given angle.
(a) −35°
(b)
5π
8
65. Give the exact value of the six trigonometric functions for each angle.
(a)
5π
(b)
6
4π
3
66.. For each, find 2 distinct values between 0 and 2pi (in radians) without a calculator.



(a) Cos −1  −
3

2 
(b) Arcsin
3
2
67. For each, find 2 distinct values in degrees between 0 and 360 (round to the nearest whole degree):
(a) sin (.85)
−1
(b) sin (−.47)
−1
(c) arccos(.91)
(d) arcsin(2.78)
68.
69.
Solve the triangle and find all missing sides and angles.
70.
Solve for side c.
71. Solve for the missing side