MATH 122:   TRIG EQUATIONS

Solve for x, y, t, or θ

  1. tan x + 1 = 0
  2. 2 sin x - 1 = 0
  3. square-root of 3 times sine x minus 2 = 0
  4. cotangent of (x plus 1) - square root of 3 = 0
  5. 4 sin2t - 1 = 0
  6. 2 tan x - 2 cot x + 3 = 0
  7. 2 cos2θ - 1 = 0
  8. sin2y + 2 sin y = 0
  9. cotangent (x plus1) minus square root of 3 = 0
  10. 2 sin2x + sin x - 1 = 0
  1. 3 tan2x - 1 = 0
  2. (sin of y) squared = square root of 3 times sin y times cos y

Equations involving multiple angles. Find all solutions in [0, 2π) or [0, 360°)

  1. sin 2θ + 2 sin θ = 0
  2. cos 2θ + cos θ + 1 = 0
  3. 4 times sine of x times cosine of x = square root of 3
  4. cos 2x = cos x
  5. square root 2 times cosine of (2 times x)
  6. 3 plus 2 times square root of 3 times sine of (2 x)
  7. arcsine of (5/13) + arccosine of (4/5) = arcsine of t

 

ANSWERS: In the following, k is an integer.

  1. 3 pi over 4 + k times pi or 135 degrees + 180 degrees times k or -pi over 4 + k times pi = -45 degrees + k times 180 degrees
  2. pi over 6 + 2k pi and 5 pi over 6 + 2k pi
    or 30° + 360°k and 150° + 360°k
  3. No Solution
  4. pi over 6 - 1 + k times pi
  5. pi over 6 + k pi and 5 pi over 6 + k pi
  6. 0.46 + kπ and -1.11 + kπ
    or 26.6° + 180° k and -63.4° + 180°k
  7. pi over 4 + k pi over 2 or 45 degrees + 90 degress times pi or 45° + 90° k
  8. kπ or 180° k
  9. 2 pi over 3 + k pi or 120 degrees + 180 degrees times pi + kπ or 120° + 180° k
  10. π/6 + 2kπ, 5π/6 + 2kπ, and 3π/2 + 2kπ
    or 30° + 360° k, 150° + 360° k and 270° + 360°k
  1. pi over 6 + k times pi, 5 pi over 6 + k times pi
    or 30° + 180°k and 150° + 180°k
  2. k times pi and pi over 3 + k times pi
    or 180°k and 60° + 180°k
  3. 0 , π or 0° , 180°
  4. pi over 2, 2 pi over 3, 3 pi over 2, and 4 pi over 3
    or 90° , 120°, 240° and 270°
  5. pi over 6, pi over 3, 7 pi over 6, and 4 pi over 3
    or 30° , 60° , 210° , 240°
  6. 0, 2 pi over 3, 4 pi over 3
    or 0° , 120° , 240°
  7. 3 pi over 8, 5 pi over 8, 11 pi over 8, 13 pi over 8
    or 67.5° , 112.5° , 247.5° , 292.5°
  8. 2 pi over 3, 5 pi over 6, 5 pi over 3, 11 pi over 6
    or 120° , 150° , 300°, 330°
  9. (-5/19) times (4/5) + (12/13) times (3/5) = 16/65