Download Algebra IIAB Chapter 13 Test Review Algebra IIAB 1. Evaluate the 6

Algebra IIAB Chapter 13 Test Review
Algebra IIAB
1. Evaluate the 6 trigonometric functions of the angle 𝜃, exactly.
a.
b.
2. In a right triangle, ∠ A and ∠ B are acute. Give exact values.
a. If tan B = 2, what is cos B?
b. If tan A =
11
,
17
what is sin A?
c. If sin B =
8
,
15
what is cos B?
A
3. Solve the triangle at the right, with the given measurements.
Round to the nearest hundredths.
a. B = 45° and c = 3
C
b. A = 36° and b = 8
c. A = 67° and c = 18
B
d. B = 60° and a = 5
4. a. John stands 150 meters from a water tower and sights the top at an angle of elevation of 36°. If John’s eyes are 2 meters
above the ground, how tall is the tower? Round to the nearest meter.
b. John stands 250 meters from a water tower and sights the top at an angle of elevation of 28°. If John’s eyes are 2.6 meters
above the ground, how tall is the tower? Round to the nearest meter.
5. Draw an angle with the given measure in standard position. Then find one positive coterminal angle and one
negative coterminal angle.
a. 58°
b. 210°
c. 305°
e. –450°
d. 580°
6. Rewrite each degree measure in radians and each radian measure in degrees.
a. 18°
b. –72°
c.
5𝜋
2
d. –
9𝜋
2
7. The terminal side of θ in standard position contains each point. Find the exact values of the six trigonometric functions of θ.
a. (3, 4)
b. (8, –15)
d. (–9, –40)
c. (–4, 3)
8. Sketch each angle. Then find its reference angle.: 0° < 𝜃 < 360° 𝑎𝑛𝑑 0 < 𝜃 < 2𝜋
a. 135˚
b. 200˚
c.
𝑣2
5𝜋
3
9. a. Estimate the horizontal distance, given by the formula 𝑑 = 32 sin 2𝜃, traveled by a track and field long jumper who
jumps at an angle of 25˚ and with an initial speed of 26 feet per second.
𝑣2
b. Estimate the horizontal distance, given by the formula 𝑑 = 32 sin 2𝜃, traveled by a track and field long jumper who
jumps at an angle of 30˚ and with an initial speed of 18 feet per second.
10. Evaluate the expression in both radians and degrees.
a. cos−1 (−
√2
)
2
1
2
b. sin−1 (− )
c. tan−1 (−
√3
)
3
11. Solve each equation. Round to the nearest tenth if necessary.
a. cos θ = 0.05; 0˚ < 𝜃 < 180˚
b. tan θ = 0.22; 0˚ < 𝜃 < 180˚
d. tan θ = 10; 180˚ < 𝜃 < 270˚
e. sin θ = 0.7; 90˚ < 𝜃 < 180˚
12. Find the measure of angle θ.
a.
8
4.6
b.
θ
θ
3.35
c.
5
θ
5.1
19
c. sin θ = – 0.03; 270˚ < 𝜃 < 360˚
f. cos θ = – 0.5; 180˚ < 𝜃 < 270˚
13. Suppose I am riding my motorcycle, and preparing to jump a line of cars. If I drive 32 feet on a ramp before
jumping, and the ramp is 8 feet high, what is the angle θ of the ramp?
14. Solve each triangle.
a.
d. a = 16, b = 20, C = 54°
Turn over********
b.
e. B = 71°, c = 6, a = 11
c.
f. A = 37°, a = 20, b = 18
15. Find the area of △ABC to the nearest tenth, if necessary.
a.
b.
c. a = 4.86, b = 3 ft, c = 7 ft
d. c = 16.4, a = 10 cm, b = 7 cm