7-6 Solving Trigonometric Equations Finding what x equals

It is just like solving regular equations, but once you get solutions, you have to find corresponding angle measure. Lets try a problem then see the rules.

What are the rules? 1.“x” means give the answer in __________; “Θ” means give the answer in ___________. 2.“Solve for 0 ≤ x < 2π” means give all the answers on one pass around the unit circle. 3.“General solution” means ______________ __________________________________ 4. Guess what: Work on both sides of the equation using all the rules of algebra. That is a) _____________ or b) ___________

Is that it? Well, yes, except for one footnote. Never Never Never Never divide both sides by the same trig function to get rid of it. For example, It will eliminate answers.

Lets Try a few

7-6 Solving Trigonometric Equations Day 2

Lets go back to the solutions from yesterday and turn them into general solutions. General Solutions will help you find every single solution no matter how many times around the circle All we do is add after the answers for one time around the circle. Or for tangent answers because ___________________________________ ___________________________________

General Solution

6-5 Inverse Trig An Inverse Function What was that again?

Lets remember: What is an inverse function? What is the notation? ___________________________ In a way, you have been practicing the inverse trig process. In section 7-6, you had the trig value and found the angle.

f(x) = sin xf(x) = sin -1 x What is the problem here? ______________________________

How do we take care of that? Therefore, there are limits on the answers that you can get. Use your calculator to find cos -1 (-.5) _____________________________

Each function has a limited Range For sin -1 x, csc -1 x, tan -1 x ____________________________ For cos -1 x, sec -1 x, cot -1 x ____________________________

REMEMBER With inverse trig you give only ___________ ___________________________________ An answer in quadrant 4 such as 300  must be given as -60 . BE Careful!!

A Hint To give yourself something to remember, use the phrase “What angle has a” for the symbol -1. SO, lets try some problems.

Inverse Rule

6-5 Day 2 Inverse Trig Continued

We will now combine Inverse Trig with: Addition and Subtraction Formulas Double Angle Formulas Half Angle Formulas

Example AB