Home > PC3 > Chapter 13 > Lesson 13.1.3 > Problem13-38

13-38.

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 trouble getting started, let $u = \frac { \pi } { 2 } ( x - 5 )$.

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

$\text{sin}(u)=-\frac{4}{10}$

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

2. Graph $y=10\sin(\frac{\pi}{2}(x-5))+24$ and $y = 20$ on a graphing calculator. Use the symmetry of the graph to determine the next positive value of $x$ where $10\sin(\frac{\pi}{2}(x-5))+24=20$.