Trigonometry Equations - Precalculus II - Lecture Notes | MATH 122, Study notes of Pre-Calculus

trig equations 1 worksheet Material Type: Notes; Class: Precalculus II; Subject: Mathematics; University: Lansing Community College;

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2011/2012

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MATH 122
TRIG EQUATIONS
Solve for x, y, t, or
1. tan x + 1 = 0
2. 2 sin x - 1 = 0
3.
4.
5. 4 sin²t - 1 = 0
6. 2 tan x - 2 cot x + 3 = 0
7. 2 cos² - 1 = 0
8. sin²y + 2 sin y = 0
9.
10. 2 sin²x + sin x - 1 = 0
11. 3 tan²x - 1 = 0
12.
Equations involving multiple angles. Find all
solutions in [0,2) or [0,360)
13. sin 2 + 2 sin = 0
14. cos 2 + cos + 1 = 0
15.
16. cos 2x = cos x
17.
18.
19.
ANSWERS:
In the following, k is an integer.
1.
or
2.
or 30 + 360k and 150 + 360k
11.
or 30 + 180k and 150 + 180k
12.
or 180k and 60 + 180k
13. 0 , or 0 , 180
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MATH 122

TRIG EQUATIONS

Solve for x, y, t, or 

  1. tan x + 1 = 0
  2. 2 sin x - 1 = 0
  3. 4 sin²t - 1 = 0
  4. 2 tan x - 2 cot x + 3 = 0
  5. 2 cos² - 1 = 0
  6. sin²y + 2 sin y = 0
  7. 2 sin²x + sin x - 1 = 0
    1. 3 tan²x - 1 = 0
    Equations involving multiple angles. Find all solutions in [0,2) or [0,360)
    1. sin 2 + 2 sin  = 0
    2. cos 2 + cos  + 1 = 0
    3. cos 2x = cos x

ANSWERS:

In the following, k is an integer.

or

or 30 + 360k and 150 + 360k

or 30 + 180k and 150 + 180k

or 180k and 60 + 180k

  1. 0 ,  or 0 , 180
  1. No Solution
  2. .46 + k and -1.11 + k or 26.6 + 180 k and -63.4 + 180k
  3. or 45 + 90 k
  4. k or 180 k
    • k or 120 + 180 k
  5. and or 30 + 360 k, 150 + 360 k and 270 + 360 k

or 90 , 120 240  and 270

or 30 , 60 , 210 , 240

or 0 , 120 , 240

or 67.5 , 112.5 , 247.5 , 292.5

or 120 , 150 , 300 , 330