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Inverse trigonometric equations are solved following these steps:

  • Isolate the trig function
  • Find the reference angle
  • Leave a positive and negative sign in front of the square root function
  • Find quadrants
  • Calculate the solution(s)

Examples

Ex. 1
tanx=tan-1(1.256)

tanx = .9 <— Isolate trig function.

II, IV <— Determine quadrants.

II: π - .9 = 2.24 <— Determine solutions.
IV: 2π - .9 = 5.38

Solutions: {2.24, 5.38}

Ex. 2
tan-1(tan(3π/4))

tan-1(tan(3π/4))

tan(3π/4) <— Isolate trig function.

tan(π/4) <— Determine reference angle.

II <— Determine quadrants.

Solution: -π/4

Practice Problems

ANSWERS
1) sin(tan-1(1/2))

2) cos(sin-1(1/3))