Download Review Key 4.1-4.3

Pre – Calculus
REVIEW 4.1 – 4.3
Name _____________________________________
For numbers 1 and 2, find the exact values of the six trigonometric functions of . Reduce and rationalize when necessary.
1.
2.
Sin𝜃=
12
csc𝜃=
13
Cos𝜃=
Tan𝜃=
5
sec𝜃=
13
12
cot𝜃=
5
Sin𝜃=
13
6√85
12
13
Cos𝜃=
7√85
Tan𝜃=
12
√85
sec𝜃=
85
5
5
csc𝜃=
85
6
cot𝜃=
7
6
√85
7
7
6
For numbers 3 and 4, find the value of x. Round to the nearest tenth if necessary.
3.
20
4.
12
Cos(25°) =
𝑥
Xcos (25°) = 20
20
X=
=22.1
Tan(70°)=
𝑥
xtan(70°)=12
12
x=
=4.4
cos⁡(25°)
tan⁡(70°)
5. A pine tree casts a shadow that is 7.9 feet long when the sun is 80 above the horizon.
a) Find the height of the tree.
Tan(80°) =
𝑥
7.9
7.9tan(80°)=x
x=44.8ft
b) Later that same day, a person 6 feet tall casts a shadow of 6.7 feet long. At what angle is the sun above the horizon?
6
𝜃=ta𝑛−1 ( )
6.7
𝜃 = 42°
For numbers 6 and 7 find the measure of angle . Round to the nearest degree if necessary.
6.
7.
10
𝜃=ta𝑛−1 ( )
5
𝜃=63°
11
)
15
𝜃 = 43°
𝜃 = 𝑐𝑜𝑠 −1 (
8. Convert the angle measure.
a)
2𝜋
9
3𝜋
=40°
b) 135
4
For numbers 9 and 10, identify all angles that are coterminal with the given angle. Then find and draw one positive and one negative
angle coterminal with the given angle.
9.
5𝜋
6
17𝜋 −7𝜋
6
,
10. –60
6
300°, -420°
11. a) Find the approximate area of the shaded region. Round to the nearest tenth if necessary.
1
13𝜋
2
9
A= ∙ 72 ∙
b) Find the length of the longer arc.
S=7∙
13𝜋
9
=31.8in
=111.2𝑖𝑛2
12. A car is traveling at a speed of 55 miles per hour on tires that measure 2.6 feet in diameter.
a) Find the linear speed at the outer edge of the tire as it spins, in feet per minute.
V=
55 5280
1
∙
60
=4840ft/min
b) Find the approximate angular speed of the tires in radians per minute.
V=𝜔𝑟
𝑣
=𝜔
𝑟
4840
1.3
=3723.1 radian per min
c) Find the radius given the linear speed and the rate of rotation
v = 49.7 ft/hr
  11.2 rev/min
𝑣
r=
𝜔
change linear speed into ft/min
.828
r=
49.7
60
=.828
=.074
11.2
For numbers 13 and 14, sketch the angle and determine the reference angle.
13. 175
14.
10𝜋
3
𝜃′ =
𝜃 ′ = 5°
𝜋
3
For numbers 15 – 18, find the exact value of the expression. If undefined, write undefined.
√2
15. cos 315
2
19. csc 225√2
16. sec
3𝜋
2
=underfined
17. sin
3
=-
√3
23. Find the exact values of the five remaining trigonometric functions of .
2
cos  = − , where sin  < 0 and tan  > 0
5
5√21
√21
Sin𝜃= csc𝜃= 5
√21
2
21
sec𝜃= -
18. tan
2
𝜋
√2
4
2
21. cos (− )=
20. cot 150√3
tan𝜃=
5𝜋
5𝜋
6
√3
=-
3
22. sin =0
2√21
cot𝜃= -
21
5
2
24. Let (–5, 12) be a point on the terminal side of an angle θ in standard position. Find the exact values of the six trigonometric
functions of θ.
12
13
5
Sin𝜃=
csc𝜃=
cot𝜃= 13
cos𝜃 =
12
−12
5
tan𝜃=
−5
13
12
sec𝜃= -
13
5