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C2 Trigonometric Identities

C2 Trigonometric Identities. cos ²ø + sin ²ø = 1 So cos ²ø = 1 - sin ²ø And sin ²ø = 1 - cos ²ø. sin ø = tan ø cos ø. 1. Use this information to solve 2 cos ²ø – sinø – 1 = 0 for 0 ≤ ø ≤ 360. 2. Solve tan ø =4cosø for -180 ≤ ø ≤ 180.

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C2 Trigonometric Identities

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  1. 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

  2. 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

  3. 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 = 0.8828 or sinø = -1.1328 (no solutions) ø = 62.0º, 118º

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