MATHPOWER TM 12, WESTERN EDITION Chapter 5 Trigonometric Equations

Solving Trigonometric Equations Quadrant I Quadrant II Quadrant IIIQuadrant IV Cosine All Sine Tangent       CAST Rule Find the measure of  0 ≤  < a) cos  =     The reference angle is The angle  is found in Quadrants II and III.  and b) tan  = The reference angle is The angle  is found in Quadrants I and III.  51 0 and

Exact Values of Special Angles 5.2.3

State the exact value of each ratio: a) b) c) d) e) f) g)h) i) Finding Exact Values = undefined

Evaluate. a) b) Finding Exact Values 5.2.5

Related Angles Quadrants I II III IV

5.2.7 Solving Trigonometric Equations a)b)c) Solve for  if 0 ≤  < 2 . General Solutions Reference Angle Reference Angle Reference Angle General Solutions

5.2.8 e) f) d) Solving Trigonometric Equations Solve for  if 0 ≤  < 2 . Reference Angle Reference Angle Reference Angle General Solutions

g) Solving Trigonometric Equations h) Solve for  if 0 ≤  < 2 . Reference Angle Reference Angle

Solving Trigonometric Equations Solve for  if 0 ≤  < 2 . a)b)

c) d) e) NO solution for cos  = Reference Angle Reference Angle Solving Trigonometric Equations

f) Reference Angle: Therefore: g) The equation cannot be factored. Therefore, use the quadratic equation to find the roots: Reference Angles: Solving Trigonometric Equations

Using a Graphing Calculator to Solve Trigonometric Equations Therefore,  and 

Suggested Questions: Pages 252 and 253 1, 4, 6, 10, 15, 22, 24, 27, 32, 33 b, 34 a (graph) 35 b