Amayas O.

asked • 6d# Solve the equation below.

For the equation below, solve for the following. Do not use a calculator. (Enter your answers as a comma-separated list. If there is no solution, enter NO SOLUTION.)

sin *θ* = - rad3/2

(a) all degree solutions (Let *k* be any integer.)

*θ* =

(b) *θ* if 0° ≤ *θ* ≤ 360°

*θ* =

## 1 Expert Answer

If sinΦ = -√3/2, (it's negative) and

sinΦ = opposite side / hypotenuse

then our opposite side is negative and we are looking for an angle in **Quadrant III** and **Quadrant IV**.

Let's take the inverse sine of both sides

~~sin~~^{-1}~~(sin~~Φ) =sin^{-1} -√3/2

Φ =sin^{-1} -√3/2

Φ = -60 or **300º** in **Quadrant IV** (__Reference angle__ is 60° away from the x-axis)

The angle 60° away from the x-axis in **Quadrant III** is 180°+60 = **240°**

**Your solution is 240° and 300°**

Note: If you need to convert these degrees to radians, just put the degree with a π (pi), divide by 180, and simplify the fraction

240° = 240π/180 Then simplify the fraction 4π/3

300° = 300π/180 Then simplify the fraction 5π/3

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Mark M.

The answer is on the unit circle. Find that!5d