Download Chapter 4 Review Convert each angle: 1) 2) 210 3) 4) 2.5 rad Find

Chapter 4 Review
Convert each angle:
 3
1)
4
2) 210○
Find the exact value of sin θ, cos θ, and tan θ:
5
5) cot θ =
, sin θ < 0
12
3)
6) sec θ = 3,
3
10
4) 2.5 rad
3
< θ < 2
2
Evaluate:
 3
= _____________
4
7) cot

= ___________
3
8) sin
9) sec
 3
= ____________
2
10) tan
14
= _____________
3
11) cos
17
= ____________
6
12) csc
11
= ____________
4
13) If tan θ =
7
and cos θ > 0, find csc θ.
8
14) For what x values is the secant function undefined? Why is it undefined at these values?
15) For a given sector of a circle, we see that the arc length is 13 meters and the central angle of the
sector is 137o. What is the radius of the circle?
16) Determine the period, amplitude, phase shift, max y, and min y:
Graph the following functions:
1


17) f(x) = sec   x  
2
2

Write the equation of a function whose graph is given.
19)
20)
f(x) = -7cos(3x) + 2
18) y = 2tan(3x) – 2
Evaluate the following:
 

21) arcsin  sin

6 


  3 
22) cos  arctan 
 
 10  

  4
23) arccos  cos
  3

 

24) A 40-foot extension ladder leans against the side of a building. How high is the top of the ladder
if the angle of elevation of the ladder is 53○?
25) Find a and b for the triangle shown.
26) Find tan(θ).
27) Find the quadrant containing the terminal side of the angle t.
a.
sec t < 0 and sin t > 0
b. cot t > 0 and csc t < 0
c. cos t > 0 and tan t < 0
d. sin t > 0 and tan t < 0
28) Find 2 angles that are coterminal with
2
rad.
7
29) Find the complement and supplement of
the angle θ =
2
rad.
5
30) You are approaching a building that you know to be 110 ft tall. Let θ be the angle of elevation to
the top of the building, and let d be your distance from the base of the building.
Write θ as a function of d.
Find θ when d = 200 feet and when d = 50 feet.
31) A passenger in an airplane flying at an altitude of 37,000 feet sees two towns directly to the left of
the airplane. The angles of depression to the towns are 32○ and 76○. How far apart are the towns?
32) A ship sails away from port with a bearing of S67oE at 28 knots for 3 hours.
a) How far south and how far east is the ship from the original port?
b) What bearing does the ship need to take in order to return to the port? (Find θ)