Name: ________________________
Date: __________
ID: A
Test Review 4.1 - 4.4 Multiple Choice Identify the choice that best completes the statement or answers the question. ____
1. Given the equation below, determine two solutions such that 0° ≤ θ < 360° .
cos θ = −
3 2
a. θ = 120°, 240° b. θ = 240°, 300° c. θ = 225°, 315° d. θ = 150°, 210° e. θ = 135°, 225°
Short Answer 2. Determine the quadrant in which an angle, θ, lies if θ = 4.90 radians. 3. Determine two coterminal angles (one positive and one negative) for θ =
4. Find (if possible) the complement of
5. Find (if possible) the supplement of
π 7
3π . 4
.
11π . 13
6. Rewrite 675° in radian measure as a multiple of π. 7. Rewrite −
7π in degree measure. 18
8. Find the angle, in radians, in the figure below if S = 10 and r = 7.
9. Find the length of the arc, S, on a circle of radius 3 meters intercepted by a central angle of 210° .
Round to two decimal places.
1
Name: ________________________
ID: A
10. Find the area of the sector of the circle with radius 2 meters and central angle
11π . 6
11. A car is traveling along Route 66 at a rate of 75 miles per hour, and the diameter of its wheels are 2.4
feet. Find the number of revolutions per minute the wheels are turning. Round answer to one decimal place.
π
12. Find the point ÊÁË x, y ˜ˆ¯ on the unit circle that corresponds to the real number t = . Use your results to 4
evaluate tant . 5π
13. Find the point ÊÁË x, y ˜ˆ¯ on the unit circle that corresponds to the real number . Use your results to 6
evaluate cos t . 14. The displacement from equilibrium of an oscillating weight suspended by a spring is given by
y(t) = 2 cos 8t , where y is the displacement in centimeters and t is the time in seconds. Find the displacement when t = 0.45, rounding answer to four decimal places.
15. Find the exact value of csc θ , using the triangle shown in the figure below, if a = 7 and b = 24.
16. Given sin30° =
3 1 and cos 30° = , determine the following: 2 2
tan30° 17. Given sec θ =
10 and tan θ = 3, determine the following.
cot (90° − θ ) 18. If sinθ =
3 , find the value of θ in degrees (0 < θ < 90° ) without the aid of a calculator. 2
2
Name: ________________________
ID: A
19. Using the figure below, if θ = 34° and y = 7, determine the exact value of x.
20. Using the figure below, if θ = 16° and y = 17, determine the exact value of r.
21. Given the figure below, determine the value of sin θ .
3
Name: ________________________
ID: A
22. The point (7, 24) is on the terminal side of an angle in standard position. Determine the exact value
of cscθ .
23. The point (−5, − 12) is on the terminal side of an angle in standard position. Determine the exact
value of secθ .
24. State the quadrant in which θ lies if tanθ > 0 and cosθ > 0. 25. Determine the exact value of sin (−315° ) .
4
ID: A
Test Review 4.1 - 4.4 Answer Section MULTIPLE CHOICE 1. ANS: D
OBJ: Solve trig equations
SHORT ANSWER 2. ANS:
4th quadrant OBJ: Determine in which quadrant an angle lies 3. ANS:
11π 5π ,− 4 4
OBJ: Determine two coterminal angles (radians) 4. ANS:
5π 14
OBJ: Find the complement of an angle (radians) 5. ANS:
2π 13
OBJ: Find the complement of an angle (radians) 6. ANS:
15π 4
OBJ: Convert degree measure to radian measure 7. ANS:
−70°
OBJ: Convert radian measure to degree measure 8. ANS:
10 7 OBJ: Find measure of central angle given radius and arc length 9. ANS:
S = 11.00 meters
OBJ: Find length of arc given radius and central angle 1
ID: A 10. ANS:
A=
11π 2 m 3
OBJ: Find the area of a sector given the radius and central angle 11. ANS:
875.4 rpm OBJ: Determine revolutions per minute 12. ANS:
tant = 1
OBJ: Evaluate trig function using unit circle 13. ANS:
cos t = −
3 2
OBJ: Evaluate trig function using unit circle 14. ANS:
–1.7935 cm OBJ: Values of trig functions at any angle 15. ANS:
25 24 OBJ: Determine trig value from diagram 16. ANS:
tan30° =
3 3
OBJ: Determine trig value given sin and cos 17. ANS:
cot (90° − θ ) = 3
OBJ: Determine trig value given sec and tan 18. ANS:
θ = 60°
OBJ: Determine theta without the use of calculator 19. ANS:
x=
7 tan34°
OBJ: Determine value of variable using right-triangle trig
2
ID: A 20. ANS:
r=
17 cos 16°
OBJ: Determine value of variable using right-triangle trig 21. ANS:
sin θ = −
24 25
OBJ: Determine trig value from diagram 22. ANS:
cscθ =
25 24
OBJ: Determine value of trig function given point on terminal side 23. ANS:
secθ = −
13 5
OBJ: Determine value of trig function given point on terminal side 24. ANS:
Quadrant I OBJ: Determine quadrant given constraints 25. ANS:
2 2 OBJ: Determine exact trig value of angle
3