Question

Solve sin ( x ) = − 0.83 on 0 ≤ x < 2 π there are two solutions, a and b, with a < b and a and b in radians to 4 decimal places.

Answer 1

Answer: a = 4.1207 and b = 5.3041

Work Shown

sin(x) = -0.83

x = arcsin(-0.83) or x = pi - arcsin(-0.83)

x = -0.9791 or x = 4.1207

Since -0.9791 is not between 0 and 2pi = 6.28, we add on 2pi to get a coterminal angle.

-0.9791+2pi = 5.3041

Therefore, the two solutions to sin(x) = -0.83 are approximately 4.1207 and 5.3041 such that 0 ≤ x < 2pi and we're in radian mode.

Side note: Arcsine refers to inverse sine. On many calculators, this is denoted with a button labeled
`\sin^(-1)`