Download SHOW YOUR WORK

Practice
Date:_____________________
Name___________________________________
SHOW YOUR WORK
1 + sin v
15) (sec v + tan v)2 =
1 - sin v
Establish the identity.
1) cot · sec = csc
2) tan
· csc
= sec
Solve the problem.
16) The current I, in amperes, flowing through a
particular ac (alternating current) circuit at
time t seconds is
I = 110 sin (70 t)
Using Ohm's Law, V = IR, if a resistance of R =
50 ohms is present, what is the voltage V?
3) sin2(- ) + cos2 (- ) = 1
4) (1 + tan2 u)(1 - sin2u) = 1
5) (tan v + 1)2 + (tan v - 1)2 = 2 sec2 v
6) sec u + tan u =
Find an equation for the graph.
17)
cos u
1 - sin u
7)
tan u - 1 1 - cot u
=
tan u + 1 1 + cot u
8)
cos u
sin u
= cos u - sin u
1 + tan u 1 + cot u
9)
cot u + csc u - 1
= csc u + cot u
cot u - csc u + 1
tan u + cot u
1
=
tan u - cot u
2
sin u - cos2 u
Use a coterminal angle to find the exact value of the
expression. Do not use a calculator.
18) sin 765°
Use reference angles to find the exact value of the
expression. Do not use a calculator.
-2
11) csc
3
Find the exact value of the indicated trigonometric
function of .
1
Find cos
19) sin = , sec < 0
6
10)
and tan .
Solve the problem.
12) For what numbers x, 0
x 2 , does sin x = 0?
13) For what numbers x, 0
x 2 , does sin x = 1?
Use a coterminal angle to find the exact value of the
expression. Do not use a calculator.
20) tan 750°
Find the exact value of the expression. Do not use a
calculator.
3
21) sin (-2 ) + cos
2
Establish the identity.
cos u
1
=
14)
cos u - sin u
1 - tan u
1
A point on the terminal side of angle , is given. Find the
exact value of the indicated trigonometric function of .
22) (9, 12); Find sin .
38) 426°
Use reference angles to find the exact value of the
expression. Do not use a calculator.
5
39) sin
3
23) (18, 24); Find cos .
24) (-10, 24); Find sin .
25) (12, 16); Find csc .
Find the exact value of the expression. Do not use a
calculator.
-5
26) cos (3 ) + sin
2
27) tan
15
4
- cos
15
4
1
, find the exact
12
value of f(a) + f(a - 2 ) + f(a + 4 ).
< 0,
cos
>0
32) csc
> 0,
sec
>0
33) sec
< 0,
tan
<0
34) tan
< 0,
sin
<0
41) tan
-7
4
42) csc
-2
3
44) A building 270 feet tall casts a 30 foot long
shadow. If a person stands at the end of the
shadow and looks up to the top of the
building, what is the angle of the person's eyes
to the top of the building (to the nearest
hundredth of a degree)? (Assume the person's
eyes are 6 feet above ground level.)
Let be an angle in standard position. Name the quadrant
in which the angle lies.
30) sin > 0,
cos < 0
31) cot
-5
6
Solve the problem.
43) A surveyor is measuring the distance across a
small lake. He has set up his transit on one side
of the lake 130 feet from a piling that is directly
across from a pier on the other side of the lake.
From his transit, the angle between the piling
and the pier is 50°. What is the distance
between the piling and the pier to the nearest
foot?
Solve the problem.
28) If f( ) = tan and f(a) = 4, find the exact value
of f(a) + f(a + ) + f(a + 3 ).
29) If f(x) = cos x and f(a) = -
40) tan
45) A radio transmission tower is 140 feet tall.
How long should a guy wire be if it is to be
attached 13 feet from the top and is to make an
angle of 35° with the ground? Give your
answer to the nearest tenth of a foot.
Find the reference angle for the given angle.
35) 29°
36) 214.3°
37) -37.4°
2