Evaluating Trig Functions

Evaluating Trig Functions of Any Angle — Extending the Trig Ratio

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    \[\sin(\theta)=\frac{y}{r}\]

    \[\cos(\theta)=\frac{x}{r}\]

    \[\tan(\theta)=\frac{y}{x}\]

Use the Pythagorean Theorem to find r=5

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    \[x=-4 , y=3, r=5\]

    \[\sin(\theta)=\frac{3}{5}\]

    \[\cos(\theta)=-\frac{4}{5}\]

    \[\tan(\theta)=\frac{3}{4}\]

 

Find the trig values for point (-12,5)

x=-12, y=5

Use the Pythagorean Theorem to find r=13

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    \[\sin(\theta)=\frac{5}{13}=\]

    \[\cos(\theta)=\frac{-12}{13}=\]

    \[\tan(\theta)=\frac{5}{-12}=\]

    \[\theta = ?\]

— If we solve with the traditional method we get the wrong answer… check reference angles to figure it out!!