Trigonometry Handout

Trigonometry
Extra Problems
1. A circle has a radius of r cm. If θ = 3 rad, and the arc a = 33 cm, then what is the
radius of the circle, r?
2. The angle of elevation of a tree 219 feet away is 17 degrees. Find the number of feet
in the height of the tree. Give your answer to the nearest integer.
3. In a right triangle, a = 39 cm, b = 36 cm and c = 15 cm. Find cot θ .
c
a
b
4. Using the same right triangle from problem 3, but now with a = 37 cm, b = 35cm, and
c = 12 cm, find sec θ .
1 1
5. The trigonometric function −
1−
sin(3x ) 1+
sin(3x)
is equal to which of the
following:
a) 2sec(3x )cot(3x)
b) 2cot(6x )csc(3x)
c) 2sec(3x
)csc(3x)
d) sec( 3x ) tan(3x)
e) 2sec(3x
) tan(3x)
1+
sin(6x)
1−
sin(6x)
6. The trigonometric function − is equal to which of the
1−
sin(6x)
1+
sin(6x)
following:
a) 2sec(6x ) tan(6x)
b) 4cot(12x )csc(6x)
c) 4sec(6x
)cot(6x)
d) sec( 6x ) tan(6x)
e) 4 tan(6x
)sec(6x)
8
15
5
7. If sin p = , cos p = , sin q = , and cos q = 12 . Find sin( q − p)
. Express your
17
17
13
13
answer as a common fraction.
8. Two straight railways cross each other at angle θ = 33 . Two trains A and B leave the
intersection O at the same time. The velocity of train A is 29 mph and the velocity of
train B is 57 mph. Find the distance between the two trains after 5 hours. Give your
answer to the nearest integer. The picture is not drawn to scale.
A
θ
o
O
θ
B
Page 21 of 23