Download Algebra II: Trig 1 Study Guide

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Algebra II: Trig 1 Study Guide
Short Answer
1. Find the measure of the angle below.
Sketch the angle in standard position.
2.
55º
3. –150º
4. Find the measure of an angle between 0º and 360º coterminal with an angle of –110º in standard position.
5. In navigation, a bearing is the angle of a course, measured in a clockwise direction, from due north. Find the
positive angle in standard position for a ship’s bearing of 320º.
6. In which quadrant does the terminal side of a 118º angle lie?
7. Find the cosine and sine of 240º. Round your answers to the nearest hundredth if necessary.
8. Find the exact value of cos 300º and sin 300º.
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9. For an angle in standard position measuring –163º, find the values of cos θ and sin θ . Round your answers
to the nearest hundredth.
10. For an angle in standard position measuring 92º, find the values of cos θ and sinθ . Round your answers to
the nearest hundredth.
Write the measure in radians. Express the answer in terms of π.
11. 320º
12. 45º
Write the measure in degrees.
13.
3π
radians
5
14. –
7π
radians
4
15. Find the degree measure of an angle of 4.23 radians.
ÊÁ 3π
Ê
ˆ˜
ˆ
˜˜ and sin ÁÁÁ 3π radians ˜˜˜ .
radians
Á
˜
˜˜
ÁË 4
ÁË 4
˜¯
¯
16. Find the exact values of cos ÁÁÁ
17. A weather satellite in circular orbit around Earth completes one orbit every 5 hours. The radius of Earth is
about 6,400 km and the satellite is positioned 4,700 km above the Earth. How far does the satellite travel in 1
hour? Round your answer to the nearest kilometer.
18. A Ferris wheel has a radius of 80 feet. Two particular cars are located such that the central angle between
them is 165º. To the nearest tenth, what is the measure of the intercepted arc between those two cars on the
Ferris wheel?
19. The line of sight from a small boat to the light at the top of a 35-foot lighthouse built on a cliff 25 feet above
the water makes a 25° angle with the water. To the nearest foot, how far is the boat from the cliff?
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20. In ∆XYZ, ∠Y is a right angle and sin X =
ID: A
20
. Find cos X in fraction and in decimal form. Round to the
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nearest hundredth, if necessary.
Find the length x. Round to the nearest tenth.
21.
22.
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ID: A
23.
24. In ∆ABC , ∠C is a right angle. Find m∠B to the nearest tenth of a degree.
Find the angle measure to the nearest tenth of a degree.
25. sin −1 0.2026
26. cos −1 0.0682
27. tan −1 7.9321
In ∆ABC , ∠C is a right angle. Find the remaining sides and angles. Round your answers to the nearest
tenth.
28. a = 3.4, c = 5.8
29. Howard is flying a kite and wants to find its angle of elevation. The string on the kite is 32 meters long and
the kite is level with the top of a building that he knows is 28 meters high.
a. Draw a diagram of the situation.
b. To the nearest tenth of a degree, find the angle of elevation. Show your work.
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Algebra II: Trig 1 Study Guide
Answer Section
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13-2.1 Working With Angles in Standard Position
13-2.1 Working With Angles in Standard Position
13-2.1 Working With Angles in Standard Position
13-2.1 Working With Angles in Standard Position
13-2.1 Working With Angles in Standard Position
13-2.1 Working With Angles in Standard Position
13-2.2 Using the Unit Circle
13-2.2 Using the Unit Circle
13-2.2 Using the Unit Circle
13-2.2 Using the Unit Circle
13-3.1 Using Radian Measure
13-3.1 Using Radian Measure
13-3.1 Using Radian Measure
13-3.1 Using Radian Measure
13-3.1 Using Radian Measure
13-3.1 Using Radian Measure
13-3.2 Finding the Length of an Arc
13-3.2 Finding the Length of an Arc
14-3.1 Finding the Lengths of Sides in a Right Triangle
14-3.1 Finding the Lengths of Sides in a Right Triangle
14-3.1 Finding the Lengths of Sides in a Right Triangle
14-3.1 Finding the Lengths of Sides in a Right Triangle
14-3.1 Finding the Lengths of Sides in a Right Triangle
14-3.2 Finding the Measures of Angles in a Right Triangle
14-3.2 Finding the Measures of Angles in a Right Triangle
14-3.2 Finding the Measures of Angles in a Right Triangle
14-3.2 Finding the Measures of Angles in a Right Triangle
14-3.2 Finding the Measures of Angles in a Right Triangle
14-3.2 Finding the Measures of Angles in a Right Triangle
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