# Midterm Exam Review Units 3-4

```NAME:_______________________________________________
Topics in Pre-Calc II – Midterm Exam Review: Units 3-4 (Trigonometry I-II)
DATE:_________
PERIOD:_______
Unit 3: Trigonometry I (Calculators Allowed)
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Using Trig Ratios to Find Sides and Angles of Right Triangles
Using the Pythagorean Theorem to Find a Missing Side of a Right Triangle
Using Reciprocal Trig Functions to Find Sides of Right Triangles
Angles of Rotation and Reference Angles
1. In figure 7, if 𝜃 = 44&deg;, what is the value of c?
(A)
(B)
(C)
(D)
(E)
6.94
7.19
9.66
10.36
13.90
2. In right triangle PQR, sin P = 0.5. What is the length of side QR?
(A)
(B)
(C)
(D)
(E)
2
3
5
6
12
3. The height of a vertical cliff is 450 m. The angle of elevation from a ship to the top of the cliff is 23&deg;. The
ship is x metres from the bottom of the cliff.
(a)
Draw and label a diagram to show this information.
(b)
Calculate the value of x.
4. Andrew is at point A in a park. A deer is 3 km directly north of Andrew, at point D. Brian is 1.8 km due
west of Andrew, at point B.
(a)
Draw a diagram to represent this information.
(b)
Calculate the distance between Brian and the deer.
(c)
Brian looks at Andrew, and then turns through an angle θ to look at the deer. Calculate the value
of θ to the nearest minute.
5. In the diagram of ABC shown below, BC = 9 and AB = 15.
To the nearest ten minutes, what is the measure of the smallest acute angle in the triangle?
6. If
1) I
2) II
3) III
4) IV
and
lie?
7. If
, in which quadrants may angle
terminate?
1) I, II
2) II, III
3) I, III
4) I, IV
8. Draw and label an angle with the given measure in standard position:
110&deg;
450&deg;
−900&deg;
−10&deg;
9. Find the reference angle, in degrees, for the following measures of 𝜃:
𝜃 = −130&deg;
𝜃=
5𝜋
3
10. Express the following as a function of a positive acute angle.
(a) cos(280&deg;)
(b) csc(−250&deg;)
11. Find the values of the six trigonometric functions for angle 𝜃 in standard position if a point with the
coordinates (5, -12) lies on its terminal side.
12. If csc 𝜃 = −2 and 𝜃 lies in Quadrant III, find tan 𝜃.
13. Find the value of each function, rounded to three significant figures.
(a) cos(17&deg;40′ 15.077′′ )
(b)
csc  118
(c)
cot  4920'
14. A person measures the angle of depression from the top of a wall to a point on the ground. The point is located
on level ground 70 feet from the base of the wall and the angle of depression is 47&deg;12’. How high is the wall, to the
nearest tenth of a foot?
15. An art student wants to make a string collage by connecting six equally spaced points on the circumference of a
circle to its center with string. What would be the radian measure, in terms of 𝜋, of the angle between two adjacent
pieces of string?
16. What is the radian measure of the larger angle formed by the hands of a clock at 8:00 p.m.?
17. The following diagram shows a carton in the shape of a cube 8 cm long on each side:
B
C
D
A
F
E
G
H
(a)
The longest rod that will fit on the bottom of the carton would go from E to G. Find the length l
of this rod.
(b)
Find the length L of the longest rod that would fit inside the carton.
Unit 4: Trigonometry II (No Calculators Allowed)
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Memorize the Entire Unit Circle (Degrees, Radians, Coordinates)
Find the Exact Value of all 6 Trig Functions (Degrees and Radians)
DIRECTIONS: Find the exact value of each trig function in simplest radical form
sin(𝜋)
cos(135&deg;)
csc(60&deg;)
tan(180&deg;)
𝜋
sec(− )
2
cot(−150&deg;)
sin(0&deg;)
tan(−
4𝜋
)
3
cos(315&deg;)
5𝜋
)
6
7𝜋
tan ( )
4
𝜋
cos(− )
3
sin(135&deg;)
11𝜋
csc (
)
6
cot(−360&deg;)
tan(−𝜋)
csc(−330&deg;)
sin(−
sec (−
5𝜋
)
4
cos(6𝜋)
tan(450&deg;)
cos (
23𝜋
)
4
10𝜋
)
3
11𝜋
cot (
)
4
csc(−720&deg;)
sec(630&deg;)
sin(−
25𝜋
sin(
)
6
cot (−
9𝜋
)
2
Given the coordinates: (0,1)
Given the coordinates: (
√2 √2
,− )
2
2
Given the coordinates: (
Find the angle in degrees:
√3 1
, )
2 2
Given the coordinates: (−1,0)
1 √3
Given the coordinates: (− , )
2 2