### Home > PC > Chapter 6 > Lesson 6.1.3 > Problem 6-41

Many times when we are solving trigonometric equations, the solutions are not convenient values on the unit circle where we can find the exact answers. For example, when we solve 2 sin

*x*= 1, we get*x*= sin^{−1}and we know the exact solution between − and is . The other solution between 0 and 2 *π*is. But what happens when we try to solve 5 sin *x*= 4? Homework Help ✎Solve 5 sin

*x*= 4 for*x*and calculate a decimal approximation.Is this the only solution between 0 and 2

*π*? Use what you know about the symmetry of the sine wave to determine the other solution between 0 and 2*π*to this trigonometric equation.Using the same method, find all of the solutions for the domain (−∞, ∞).

Use the unit circle and symmetry.

How can you write this?

*x* = 0.927*x* = π − 0.927

Add 2π*n* where *n* = any integer to both answers above.