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**C2 Trigonometric Identities**

cos²ø + sin²ø = 1 So cos²ø = 1 - sin²ø And sin²ø = 1 - cos²ø sin ø = tan ø cos ø 1. Use this information to solve 2 cos²ø – sinø – 1 = 0 for 0 ≤ ø ≤ 360 2. Solve tanø =4cosø for -180 ≤ ø ≤ 180

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2 cos²ø – sinø – 1 = 0 for 0 ≤ ø ≤ 360 Cos²ø = 1 - sin²ø 2(1 - sin²ø) – sinø – 1=0 2 - 2sin²ø – sinø – 1=0 2sin²ø + sinø – 1=0 Factorise (2sinø - 1)(sinø + 1)=0 sinø = ½ or sinø = -1 ø = 30º, 150º or 270º

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**Solve tanø =4cosø for -180 ≤ ø ≤ 180**

sin ø = 4cosø cos ø sinø = 4cos²ø sinø = 4(1-sin²ø) sinø = 4 - 4sin²ø 4sin²ø – sinø – 4 = 0 (use formula to solve) sinø = or sinø = (no solutions) ø = 62.0º, 118º

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Section 7.5 Solving Trigonometric Equations Copyright ©2013, 2009, 2006, 2001 Pearson Education, Inc.

Section 7.5 Solving Trigonometric Equations Copyright ©2013, 2009, 2006, 2001 Pearson Education, Inc.

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