-11+24sin theta = 16cos^2theta

Question

use graphing utility to find exact solution. should be 2 answers?

Answer 1

If you graph two trig functions on the same coordinate grid, it will be difficult to see the points of intersection.  So we will write the two functions as a single function.

 

Bring all terms to the left side.  Let       x = theta

 

24sinx - 16cos²x - 11 = 0

 

 

Write in only in terms of sine or cosine.

 

24sinx - 16(1 - sin²x) - 11 = 0

 

16sin²x + 24sinx - 27 = 0

 

 

Now, we graph on the calculator.  Press Y= .  Enter the function      (16sin²x + 24sinx - 27).  Press GRAPH.  See your sine wave being constructed.  Then press 2ND and TRACE.  Select zero.  You will then be asked to pick your left and right bounds of the zero.  Choose any left and right bound.  Then press ENTER.  Read the x-coordinate at the bottom of the screen.  That is one solution.  Repeat the process to get the other zero.