C2 Trigonometric Identities

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# C2 Trigonometric Identities - PowerPoint PPT Presentation

2 cos?? ? sin? ? 1 = 0 for 0 = ? = 360. Cos?? = 1 - sin??. 2(1 - sin??) ? sin? ? 1=0. 2 - 2sin?? ? sin? ? 1=0. 2sin?? sin? ? 1=0. Factorise (2sin? - 1)(sin? 1)=0. sin? = ? or sin? = -1. ? = 30?, 150? or 270?. Solve tan? =4cos? for -180 = ? = 180. sin ? = 4cos?cos ?. sin? = 4cos??. sin? = 4(1-s

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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

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

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