11. Solving Trig Equations

We’ll do the same things today as yesterday but today instead of x as the variable, we’ll have trig functions as the variable

Example: Solve for the variable.

Always look for a GCF first!

Difference of Squares

Factoring Trinomials

3tan2 x– 14tanx + 8 1) Multiply 3 • (8) = 24; tanx2- 14tanx + 24 2) Set up ( ) ( tanx )( tanx ) 3 3 What multiplies to 24 and adds to -14? ( tanx - 12)( tanx - 2) 3 4) Simplify (if possible). 5) Move denominator(s)in front of “x”. ( tanx - 4)( 3tanx - 2)

2sec2 x– 3secx – 9 1) Multiply 2 • (-9) = -18; secx2 – 3secx - 18 2) Set up ( ) ( secx )( secx ) 2 2 What multiplies to -18 and adds to -3? ( secx - 6)( secx + 3) 2 4) Simplify (if possible). 5) Move denominator(s)in front of “x”. ( secx - 3)( 2secx + 3)

6sin3x + 13sin2x + 6sinx 1) Factor GCF sinx(6sin2x + 13sinx + 6) 2) Multiply 6 • (6) = 36; Sinx(sin2x + 13sinx + 36) 3) Set up ( ) sinx( sinx )( sinx ) 6 6 4) What multiplies to 36 and adds to 13? sinx(sin x + 4)( sinx + 9) 6 5) Simplify (if possible). 5) Move denominator(s)in front of “x”. sinx(3sinx + 2)( 2sinx + 3)

Practice before finishing the rest of the notes!!

To finish solving Trig Equations Solve the equation like normal, then look on unit circle to find angle

Notations for answers If the problem says “find solutions between or “, then you will have a specific answer (or 2) If the problem says “find ALL solutions”, add 360n OR 2πn to every answer

INVERSE TRIG. RESTRICTIONS Remember to use inverse trig restrictions!! Sin, csc, tan, cot are in the 1st and 4th quadrants Cos and sec are in the 1st and 2nd quadrants

HELPFUL HINTS

Example Find all solutions in degrees

Example Find all solutions in radians

Example Find all solutions in degrees

Example Find solutions in