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BELLWORK: Factor the following expressions:

Learn how to factor and rewrite trigonometric equations, considering domain restrictions and using fundamental and reciprocal identities. Solve for multiple solution intervals.

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BELLWORK: Factor the following expressions:

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  1. BELLWORK: • Factor the following expressions:

  2. 1. If the equation is already in terms of just ONEtype of trig function • -move all terms to one side and set equation = 0 • -FACTOR • -set each factor = 0 and solve • -make sure you check your answers for extraneous solutions If the equation has MORE THAN ONE type of trig function, you must try to REWRITE AND REPLACE one trig function with another. There are LOTS of IDENTITIES that help us rewrite functions. Solving Trig Equations:Part 2Factoring and Rewriting as one Trig Function

  3. You must consider any restrictions on the domain. • [0,2π) is just one time around the circle, so only consider each quadrant once. • [0,3π] is one and a half times around the circle, so you consider all 4 quadrants plus 1st and 2nd quadrants AGAIN. • [0,8π] is 4 times around the circle, so all quadrants are considered 4 times. • [0,∞) requires that you continue the cycle FOREVER. In this case, we add a generic ending of πn or 2πn to our answers. Restrictions and Infinite Solutions

  4. Example 1) Find all solutions for the equation

  5. Example 2) Find all solutions for the equation

  6. Ex 3) Solve for the intervals of a) [0,2π) b) [0,3 π) c) [0,∞)

  7. Fundamental Identities: -help us rewrite functions that CAN NOT be factored or simplified Reciprocal Identities

  8. Goal = simplify to ONE trig function Where to start? = rewrite everything in terms of sin and cos Examples: cot(x)sec(x) 2. 3. 4.

  9. Pythagorean Identity Proof

  10. Additional Pythagorean Identities **Don’t memorize the extras. Understand how to get to extras by using the original. 1. Divide all terms by x 2. Divide all terms by x

  11. Replace one of your trig functions so we only have to deal with one type. Pythagorean Identity Distribute Simplify Factor

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