5.2 Solving Trig Ratios for Any Angle

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5.2 Trigonometric Ratios of Any Angle

Mental MathFind cosθ of the following triangle; leave as an exact value

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4θ

5.2 Solving Trig Ratios for Any Angle

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Finding the Trig Ratios of Any Angle Θ, where 0°≤Θ≤360°

Suppose θ is any angle in standard position...

.P(x, y)θ

5.2 Solving Trig Ratios for Any Angle

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Finding the Trig Ratios of Any Angle Θ, where 0°≤Θ≤360°

.P(x, y)θ

sinθ =

cosθ =

tanθ =

5.2 Solving Trig Ratios for Any Angle

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5.2 Solving Trig Ratios for Any Angle

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E.g. The point P(8, 15) lies on the terminal arm of an angle, θ, in standard position. Determine the exact trigonometric ratios for sinθ, cosθ, tanθ

5.2 Solving Trig Ratios for Any Angle

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5.2 Solving Trig Ratios for Any Angle

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CAST Rule

5.2 Solving Trig Ratios for Any Angle

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E.g. Determine the exact value of cos135°.

5.2 Solving Trig Ratios for Any Angle

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5.2 Solving Trig Ratios for Any Angle

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E.g. Suppose θ is an angle in standard position with terminal arm in quadrant III, and cosθ = ­3/4. What are the exact values of sinθ and tanθ?

5.2 Solving Trig Ratios for Any Angle

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5.2 Solving Trig Ratios for Any Angle

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The quadrantal angle is an angle in standard position whose terminal arm lies on one of the axes.

5.2 Solving Trig Ratios for Any Angle

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P(0, y)

r = y

Let's find the trig ratios if θ=90°

5.2 Solving Trig Ratios for Any Angle

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180

5.2 Solving Trig Ratios for Any Angle

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Homeworkp 96#1­6