8-5

8-5 is almost exactly like 8-1.
***You can not divide by a trig function to cancel it on both sides in an equation. You must move it to the other side and factor it out.***
I will tell/show you the steps as I work the problem.

Ex.1: 8sin^2x-4=0

• First, you have to get the trig function by itself. You subtract 4 on both sides leaving you with 8sin^2x=4.
• Now you have to divide by 8 on both sides leaving you with sin^2x=4/8 which equals to sin^2x=1/2.
• After you do that, you have to take the square root on both sides. That gives you sinx=the square root of 1/2 which equals to sinx=+-square root of 2/2.
• Now you solve for x which gives you x=sin-1(+-square root of 2/2). When you are solving for x, you take the inverse of sin.
• Now you have to find what quadrant it is in. Sin-1(+-square root of 2/2)=45. So 45 is in quadrant one and since it is a positive and negative answer, you have to find all of the quadrants.
• Quadrant 2: -45+180=135. Quadrant 3: 45+180=225. Quadrant 4: -45+360=315. Your final answer: X=45 degrees, 135 degrees, 225 degrees, 315 degrees.

Ex.2: 6sinx=cosx for 0 degrees less than or equal to x less than or equal to 360 degrees

• First, you have to divide by cosx on both sides leaving you with 6sinx/cosx=1.
• Now you can change 6sinx/cosx to 6tanx so that gives you 6tanx=1.
• Then you have to divide by 6 on both sides which gives you tanx=1/6.
• Now solve for x: x=tan-1(1/6). tan-1(1/6)=9.462 which is in quadrant one.
• Now you have to find the quadrants where tan is positive. Tan is positive in one and three. We already found quadrant one so now we have to find quadrant three. Quadrant three: 9.462+180=189.462.
• Now you have to put those answers into degrees minutes and seconds. Quadrant one: .462x60=27.72, .72x60=43.2. Quadrant three: .462x60=27.72, .72x60=43.2.
• Final answer: X= 9 degrees 27 minutes 43 seconds, 189 degrees 27 minutes 43 seconds

Amber :)