Download Math 4 - El Camino College

Math 170 – Trigonometry
Sample Big Test #3
1.
Evaluate each of these expressions exactly, without using a calculator (except for basic
arithmetic). A diagram (or two) may be helpful.
3
2
a)
sin2arctan7
b)
cos2arccos5

 

 
3
-1
c)
cosarcsin5 + arccos 2 

 
 
2.
Find all degree solutions of this equation:
3.
Find all radian solutions such that 0  t < 2 :
4.
Find all solutions (exact values only) of this equation: 3sinx - 10cotx = -9cscx
5.
Solve this equation for θ if 0 ≤ θ < 360:
6.
Find all solutions in radians using exact values only.
3
+ 5sin = 3sin.
cosx – 2sinxcosx = 0
2sinθ = sin2θ
-1
sin2xcos3x + cos2xsin3x = 2
7.
Find all solutions if 0 ≤ θ < 360. If necessary, round your answers to the nearest
tenth of a degree.
2
3cos 3θ + 10cos3θ – 12 = 0
8.
The bell tower of the cathedral in Pisa, Italy leans 5.6 from the vertical. A tourist
stands 105 m from its base, with the tower leaning directly towards her. She measures
the angle of elevation to the top of the tower to be 29.2. Find the length of the tower.
Give both an exact answer (i.e. before you have used your calculator) and one rounded
to the nearest meter. (Please draw a figure and label it well.)
9.
The following information refers to triangle ABC. Sketch the triangle and then solve it
using the Law of Sines.
∠A = 23 ,
10.
∠B = 110, c = 50
Show that this is an identity by transforming one side into the other. Justify each of
your steps.
2
1 - tan 
cos2 =
2
1 + tan 
11.
-3
If sin = 7
a)
12.
and
180 <  < 270 , find the following. (Show all of your work.):
sin2
b)

sin2
 
Prove the following identity. Be sure to show your justifications for each step.
sin( + ) + sin( – ) = 2sin cos 7h
13.
The following information refers to triangle ABC. Sketch the triangle and then solve it
using the Law of Sines.
∠A = 62.1 , a = 7.31 feet,
14.
b = 8.11 feet
The following information refers to triangle ABC. Sketch the triangle and then solve it
using the Law of Cosines. Give the angles to the nearest degree.
a = 66 cm, b = 120 cm, c = 72 cm
15.
The following information refers to triangle ABC. Sketch the triangle and then solve it
using the Law of Cosines. Give the angles to the nearest degree and the sides to the
nearest inch.
a = 45 inches, ∠B = 42, c = 33 inches