Worksheet over 5.4 to 5.6
Please DO NOT PRINT THIS!!! Show all your work on a seperate sheet.
Prove the identity.
1) cos 3x = cos3 x - 3 sin2 x cos x
1)
2) 4 csc 2x = 2 csc2 x tan x
2)
Find all solutions to the equation in the interval [0, 2 ).
3) cos 2x - cos x = 0
4) 2 cos x + sin 2x = 0
Rewrite with only sin x and cos x.
5) cos 2x + sin x
3)
4)
5)
6) sin 3x - cos x
6)
7) sin 2x - cos 3x
7)
Find the exact value by using a half-angle identity.
8) sin 22.5°
9) tan 75°
10) sin
7
8
Solve the triangle.
11)
8)
9)
10)
11)
12) B = 73°, b = 15, c = 10
12)
The given measurements may or may not determine a triangle. If not, then state that no triangle is formed. If a triangle is
formed, then use the Law of Sines to solve the triangle, if it is possible, or state that the Law of Sines cannot be used.
13) C = 37°, a = 19, c = 8
13)
14) B = 111°, c = 8, b = 12
14)
15)
15)
20
49°
Solve.
29
16) Points A and B are on opposite sides of a lake. A point C is 88.4 meters from A. The
measure of angle BAC is 71°20', and the measure of angle ACB is determined to be 30°30'.
Find the distance between points A and B (to the nearest meter).
16)
17) A ranger in fire tower A spots a fire at a direction of 40°. A ranger in fire tower B, which is
28 miles directly east of tower A, spots the same fire at a direction of 116°. How far from
tower A is the fire?
17)
Solve the triangle.
18)
18)
19) a = 9, b = 15, c = 4
19)
20) a = 5, b = 11, c = 9
20)
Find the area. Round your answer to the nearest hundredth if necessary.
21) Find the area of the triangle with the following measurements:
A = 50°, b = 31 ft, c = 18 ft
2
21)
Decide whether a triangle can be formed with the given side lengths. If so, use Heron's formula to find the area of the
triangle.
22) a = 58
22)
b = 65.4
c = 56.9
23) a = 31
b = 20.6
c = 8.4
23)
Solve the problem.
24) An airplane leaves an airport and flies due west 120 miles and then 150 miles in the
direction S 39.17°W. How far is the plane from the airport at this time (to the nearest mile)?
25) A building has a ramp to its front doors to accommodate the handicapped. If the distance
from the building to the end of the ramp is 19 feet and the height from the ground to the
front doors is 4 feet, how long is the ramp? (Round to the nearest tenth.)
3
24)
25)
Answer Key
Testname: PC LESSON 5.4 TO 5.6 PRACTICE
1) cos 3x = cos (2x + x) = cos 2x cos x - sin 2x sin x = (cos2 x - sin2 x) cos x - 2 sin x cos x sin x =
cos3 x - sin2 x cos x - 2 sin2 x cos x = cos3 x - 3 sin2 x cos x.
2) 4 csc 2x =
3) 0,
2 4
,
3 3
4)
,
2
4
2 sin x
=
= 2 csc 2 x tan x.
2 sin x cos x sin 2 x cos x
3
2
5) 1 - 2 sin2 x + sin x
6) 2 sin x cos2 x + sin x - 2 sin3 x - cos x
7) 2 sin x cos x + cos x - 4 cos x sin2 x
8)
1
2
2-
9) 2 + 3
1
210)
2
11)
12)
13)
14)
15)
16)
17)
18)
19)
20)
21)
22)
23)
24)
25)
2
2
C = 75°, c 4.2, a 3.8
C = 39.6°, A = 67.4°, a 14.5
No triangle is formed.
C = 38.5°, A = 30.5°, a 6.5
The triangle cannot be solved with the Law of Sines.
46 m
26 miles
B = 34.7 , C = 20.3 , a = 21.5
No triangles possible
A 26.6°, B 99.6°, C 53.8°
213.73 ft2
1544.39
No triangle is formed.
244 mi
19.4 ft
4