Inverse Trig Functions

Inverse Notation y = arcsin x or y = sin-1 x Both mean the same thing. They mean that you’re looking for the angle (y) where sin y = x.

Evaluating Inverse Functions Find the exact value of: Arcsin ½ This means at what angle is the sin = ½ ? π/6 5π/6 has the same answer, but falls in QIII, so it is not correct.

Calculator When looking for an inverse answer on the calculator, use the 2nd key first, then hit sin, cos, or tan. When looking for an angle always hit the 2nd key first. Last example: Degree mode, 2nd, sin, .5 = 30.

Evaluating Inverse Functions Find the value of: sin-1 2 This means at what angle is the sin = 2 ? What does your calculator read? Why? 2 falls outside the range of a sine wave and outside the domain of the inverse sine wave

Composition of Functions Find the exact value of Where is the sine = Replace the parenthesis in the original problem with that answer Now solve

Example Find the exact value of The sine angles must be in QI or QIV, so we must use the reference angle

Example Find tan(arctan(-5)) Find If the words are the same and the inverse function is inside the parenthesis, the answer is already given!

Example Find the exact value of Steps: Draw a triangle using only the info inside the parentheses. Now use your x, y, r’s to answer the outside term 3 2

Last Example Find the exact value of Cos is negative in QII and III, but the inverse is restricted to QII. 12 -7

You Do Find the exact value of