Download 5π 2 π π 7 7 sin(θ) tan(θ) > 0 y = 5 sin( x) 3

Trigonometry
Have Fun!
1) Convert
5
to degrees.
2
2) Convert 240 to radians
3) An angle is formed by moving the terminal side clockwise into the first quadrant. The y-value of the
terminal point is ½. What is the angle that has been formed in radians?
4) Give the exact value (do not give decimal approximations) of the tan 60 and the sec 60 .
5) Evaluate the expressions by using a calculator of tan


and sec .
7
7
6) Determine whether the following is true or false:
If sin  = 0.254, then csc = 2.581.
7) The builder of a parking garage wants to build a ramp at an angle of 17 degrees that covers a
horizontal span of 50 feet. How long will the actual ramp be?
8) What quadrant must  be in if
sin( )  0
and
tan( )  0
9) What is the reference angle for 570 ?
10) Determine the amplitude, period, and phase shift of:
5
y  sin( x)
3
If there is no phase shift, state “no phase shift”. If there is a phase shift, state the direction of the phase
shift and the number of units (as a positive number) the graph is shifted.
11) Determine the amplitude, period, and phase shift of:
2
y  cos(9x)
3
If there is no phase shift, state “no phase shift”. If there is a phase shift, state the direction of the phase
shift and the number of units (as a positive number) the graph is shifted.
12) Jennifer is watching a satellite launch from an observation spot 2 miles away. Find the angle of
elevation from Jennifer to the satellite, which is at a height of 1.1 miles. Write your answer in degrees.
13) Show that tan 2 x  tan 2 xsin 2 x  sin 2 x
14) Find the exact value (decimal answers are not accepted) of cos
13
.
12
15) Determine the exact value (decimal answers are not accepted) of sin
17
.
6
16) Solve for x. Indicate all possible solutions. Use the variable n to represent any integer multiple of
the function’s period. Write your answer in exact radians.
2 tan 2 x  6  0

17) Prove that tan(   )   tan



18) The complicated trigonometric expression shown below is equivalent to either
sin x, cos x, or tan x . Which one is it? Prove it.
3 sin( x  30 )  cos( x  30 )
4 cos x sin( x  30 )  4 sin x cos( x  30 )