Week 12 Trigonometric Functions of Any Angle.pdf - MTH117 Week 12 15.1 Trigonometric Functions of Any Angle Definition • = = ℎ = = ℎ = = = 1 1 = =

Week 12 Trigonometric Functions of Any Angle.pdf - MTH117...

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MTH117 Week 12 15.1 Trigonometric Functions of Any Angle Definition: (?𝑖?𝑒): ?𝑖?𝜃 = ? ? = ???????? ℎ????????? (𝑐??𝑖?𝑒): 𝑐??𝜃 = ? ? = 𝑎??𝑎???? ℎ????????? (?𝑎?𝑔𝑒??): ?𝑎?𝜃 = ? ? = ???????? 𝑎??𝑎???? (𝑐??𝑒𝑐𝑎??): 𝑐?𝑐𝜃 = 1 ??? 𝜃 = ? ? = ℎ????????? ???????? (?𝑒𝑐𝑎??): ?𝑒𝑐𝜃 = 1 ??? 𝜃 = ? ? = ℎ????????? 𝑎??𝑎???? (𝑐??𝑎?𝑔𝑒??): 𝑐??𝜃 = 1 ?𝑎? 𝜃 = ? ? = 𝑎??𝑎???? ???????? Example: A point of the terminal side of angle 𝜃 has the coordinates (-3, -5). Write the six trigonometric functions of 𝜃 to three significant digits. ? 2 + ? 2 = ? 2 (−3) 2 + (−5) 2 = ? 2 34 = ? 2 ? = √34 ?𝑖?𝜃 = −5 √34 𝑐??𝜃 = −3 √34 ?𝑎?𝜃 = −5 −3 = 5 3 𝑐?𝑐𝜃 = √34 −5 ?𝑒𝑐𝜃 = √34 −3 𝑐??𝜃 = −3 −5 = 3 5 ? ? ? ? ? 𝜃 (?, ?)
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