Name:
Trig Equations and Identities Practice test
Instructions:
• Support your answers with evidence of your understanding.
Show your work and circle your answer.
Part Aà 1 Mark each. Total of 6 marks.
1.
The two smallest positive
solutions of sin3x = 0.7 are
x=0.26 and x=0.79.
Determine the general
solution for sin3x = 0.7 .
Simplify:
cos 7 x cos2x + sin7 x sin2x
4.
State the exact solution
2.
tan x =
1
3
Simplify:
6.
Solve cos x sin x − 1 = 0
for 0 ≤ x < π .
5.
Cross out any that are not
true. cos 4x =
•
•
•
sin2 2x − cos2 2x
1 − cos2x
3.
sin2 x
(
)
for 0 ≤ x < π .
1 − 2sin2 2x
2cos2 8x − 1
Part Bà 2 marks each.. (16 marks)
1.
(
Determine the exact value of cot 105°
!
)
2.
(
Determine the exact value of sec 345°
!
)
1
Name:
Part B Continued: ( Most show all steps to receive credit)
3.
(
)
Simplify: cos π − x .
4.
Simplify:
tan2 x sin2x
(
2 1 − cos2 x
)
SHOW ALL WORK!
The answer is one of these: Sinx, cosx, tanx, cscx, secx or cotx
5.
Solve: 2cos2 x = cos x where 0 ≤ x < 2π .
6.
Determine the number of solutions for
(a cos x − b ) (a sin x − a ) (b cos x + a ) = 0
Exact answers only.
where 0 ≤ x < 2π , 0 < a < b .
7.
If tan x = −
3
and x is in the quadrant 2,
4
evaluate sin2x .
Exact answers only.
8.
Solve: sin2x =
1
2
Exact answers only.
, where 0 ≤ x < 2π .
Exact answers only.
2
Name:
Part C: 3 marks each.
9.
Solve: 2cos2 x − 3cos x − 2 = 0 Find the
general solution. Do not use your calculator. Exact answers
10.
Solve: 6 tan2 x − 1 = 5 , 0 ≤ x < 2π .
Do not use your
calculator. Exact answers only.
only.
11.
Solve: cos2x − 3sin x = 2 ,
not use your calculator. Exact answers only.
0 ≤ x < 2π
Do
12.
Solve: tan x sin x + tan x cos x = 0 , where
0 ≤ x < 2π . Do not use your calculator. Exact answers only.
3
Name:
Part C: àProofs must be neat. DO NOT skip steps. Clearly show every step.
13.
15.
Prove the identity:
cos x + cot x
sec x + tan x
=
cos2 x
14.
2cos x + 2cos2 x
sin x
#
π&
Prove the identity: − tan x = cot % x − (
2'
$
Prove the identity:
sin2x
16.
=
sin x
1 − cos x
Prove the identity: tan2 x −
sin4 x
cos x
2
= sin2 x
4