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Published byBrett Floyd Modified over 7 years ago

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Inverses How do we know if something has an inverse? ○ Vertical line tests tell us if something is a function ○ Horizontal line tests will tell us if there is an inverse. Do any of the 6 trig functions have inverses? ○ What if we restricted what we were looking at…

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Inverse Sine Function “Arcsine Function”

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Evaluate without a Calculator You can only have answers between [-π/2, π/2] sin -1 ( 1 / 2 ) sin -1 (- √3 / 2 )

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Evaluate without a Calculator You can only have answers between [-π/2, π/2] sin -1 ( π / 2 ) sin -1 (sin( π / 9 )) sin -1 (sin( 5π / 6 ))

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Evaluate with a Calculator Use the “2 nd ” button and the “sin” button. sin -1 (-.081) sin -1 (sin(3.49π)) sin -1 (3)

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Inverse Cosine Function

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Evaluate without a Calculator cos -1 (- √2 / 2 ) cos -1 (cos(-1.1))

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Inverse Tangent Function

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Evaluate without a Calculator tan -1 (√3) tan -1 (-1)

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Evaluate with a Calculator sin -1 (0.362) in degrees tan -1 (-12.5) in degrees tan -1 (2.37) in radians sin -1 (-0.46) in radians

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Evaluate without a Calculator cos(sin -1 ( 1 / 2 )) sin -1 (cos( π / 4 )) arcsin(cos( π / 3 )) cos(tan -1 (√3))

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