Inverse Trig Functions Inverse Notation y arcsin x

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 2 nd key first, then hit sin, cos, or tan. • When looking for an angle always hit the 2 nd key first. • Last example: Degree mode, 2 nd, 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)) -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. 3 • Now use your x, y, r’s 2 to answer the outside term

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