Solve sin θ = 0.95 for -90º ≤ θ ≤ 90º. Round to the nearest tenth.

Question

Solve.  

 

Round to the nearest tenth.

Answer 1

sin θ = 0.95 for -90º ≤ θ ≤ 90º

 

Since the sine value is positive, θ will be in quadrant One ONLY and it will be given by any decent calculator as

  θ = arcsin 0.95

 

DO NOT ADD 360 degrees because the restriction prohibits it, in this question.

Answer 2

-90 degrees is equivalent to 270 degrees.  So the solution must be in the interval   270 ≤ θ ≤ 450

 

θ = sin^-1(0.95)

 

sine is positive in the 1st quadrant.

 

Then in the first quadrant.

 

θ = 360° + sin^-1(0.95)