Download Practice Test Ch 5

Practice Test Ch 5 pg1
Math 240
Instructor: Butler
Practice Quiz
Chapter 5
Do not use a calculator for this test.
1. Fill in the blank
a)
tan  x  = ______________ (Negative-Angle Identity)
b)
1  sin 2 x = ______________ (Pythagorean Identity)
c)
sin 2 A = _______________ (Double Angle Identity)
d)
cos 2 A = cos 2 A  sin 2 A
e)
cos
f)
sin 90    = cos
____________________
g)
tan 2   1 = sec 2 
____________________
h)
sec  = _________________ (Reciprocal Identity)
i)
cos A  B = ____________________ (Cosine Difference Identity)
j)
cot90    = __________________ (Cofunction Identity)
____________________
A
= ________________ (Half-Angle Identity)
2
2. Use the fundamental identities to find the remaining five trigonometric functions of θ.
1
cos  
a)
 in Quadrant I
5
3. Verify the identity. Show all your work, and all the steps.
a) tan   cot   sec csc
b) csc  cos 2   sin   csc 
c)
sin 2 x
2

sin x sec x
Practice Test Ch 5 pg2
4. Use the sum and difference identities to find the exact values.
5
a) cos15
b) sin
c) sin 105
12
d)
tan 80  tan 55
1  tan 80 tan 55
2
1
and sin t   , s is in quadrant II and t is in quadrant IV,
3
3
a) find coss  t 
b) find tan s  t 
c) quadrant of s  t
5. Given sin s 
6. Use a double angle or half angle identity to write each expression as a single
trigonometric function or a single number.
2 tan 15
1
1  cos 76
a)
b)
c) 1  2 sin 2 22 
2
2
1  tan 15
2
7. Find the exact value of cos
cos
x
=
2
x
5
given sin x   and tan x > 0
2
8
1  cos x
2
ANSWERS
1.a)  tan x
1.b) cos 2 x
1.f) Cofunction Id.
1.c) 2 sin Acos A
1.g) Pythagorean Id.
1.d) Double Angle Id.
1.h)
1
cos 
7. 
2. sin  
8  39
4
1  cos A
2
1.i) cos A cos B  sin A sin B
2 6
tan   2 6 sec  5 csc  
5
6 2
6 2
6 2
4.a)
4.b)
4.c)
4.d)  1 5.a)
4
4
4
3
8 5 5 2
5.b)
5.c) Quadrant II 6.a)
6.b) cos 38
3
20  2 10
1.j) tan 
1.e) 
5 6
12
cot  
 2 10  2
9
2
6.c)
2
6
12