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Warm up

Warm up. A man on a 135-ft vertical cliff looks down at an angle of 16 degrees and sees his friend. How far away is the man from his friend? How far is the friend from the base of the cliff?. Lesson 14 Inverse Functions.

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Warm up

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  1. Warm up • A man on a 135-ft vertical cliff looks down at an angle of 16 degrees and sees his friend. How far away is the man from his friend? How far is the friend from the base of the cliff?

  2. Lesson 14 Inverse Functions Objective: To introduce inverse functions and use them to find the angles of right triangles.

  3. Inverse Functions • Inverse functions sin-1 or arcsin • cos-1 or arccos • tan-1 or arctan • They are used to find the missing angle in a right triangle. • THESE ARE NOT THE SAME AS THE RECIPROCAL OF THE FUNCTION

  4. Sin-1 x =

  5. Finding the angle • To find the angle β– use one of the trig functions that you have the info for. Ex: sin β = because we don’t know the angle. β 5 3 α Press [2nd] [sin-1] (4/5) This will give you the Degrees of angle β A 4 C

  6. Examples 30o 150o -30o 45o

  7. Warm up • Find the angle – round to the nearest degree: • Sin A = .9063 • Cos B = .6428 • Tan C = .4040

  8. Using the unit circle • Inverse functions can be evaluated using the unit circle. • Only the angles between -90 and 90 are used. • Ex: sin-1 ( ) could be either 60o or 120 o, so we are taking the one that is less than 90o

  9. Find the angles using the unit Circle 60o 45o 45o

  10. Combining Functions with Inverses • means that you want to find the tangent of whatever angle has a cosine of We are only going to do this on the calculator.

  11. Practice • Cos(tan-1(.95)) = • Sin(cos-1(5/6))= • Tan(tan-1(2) = • .725 • .5528 • 2

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