### Home > PC > Chapter 6 > Lesson 6.2.2 > Problem6-86

6-86.

Now consider the equation $10 \sin( \frac { \pi } { 2 } ( x - 5 ) ) + 24 = 20$.

1. Solve the equation for the smallest positive value of $x$ (in radians). If you are having a problem getting started, let $u =\frac { \pi } { 2 }(x − 5)$. Be sure to choose the correct value of $x$.

Substituting '$u$' into the equation.
$10\sin \left(u\right) + 24 = 20$
$10\sin \left(u\right) = −4$

Using a calculator, $u = −0.4115$.
Substitute back to solve for $x$.

2. Add $y = 20$ to your graph. Use the symmetry of your graph to find the next positive value of where $10 \sin( \frac { \pi } { 2 } ( x - 5 ) ) + 24 = 20$.

3. Check your results by graphing $y = 10 \sin( \frac { \pi } { 2 } ( x - 5 ) ) + 24$ and $y = 20$ on your graphing calculator.