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Inverse Trig Functions

Inverse Trig Functions. Lesson 3.5. Start with Sine Function. Given y = sin (x) Table of values Graph. What if we reversed the ordered pairs … y for x ?. Reversed Ordered Pairs. Problem This is not a function Fails the vertical line test There are multiple (x,y)'s where x = .5

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Inverse Trig Functions

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  1. Inverse Trig Functions Lesson 3.5

  2. Start with Sine Function • Given y = sin (x) • Table of values • Graph What if we reversed the ordered pairs … y for x ?

  3. Reversed Ordered Pairs • Problem • This is not a function • Fails the vertical line test • There are multiple(x,y)'s where x = .5 • Solution • Limit the range

  4. The Inverse Trig Function • We say • Similarly for inverse cosine • The range of cos-1x is limiteddifferently • Note pg 258 for domain, range ofother functions

  5. Evaluating Inverse Functions • Consider cos-1(-0.5) • We are asking what angle has a cosine value of -0.5 • Cosine negative in quadrants 2 and 3 • But for cos-1(x) we look only in 1 & 2 Calculator also capable of evaluating inverse trig functions 2 -1

  6. Try It Out • Consider these Note: newer calculators will have these functions – find in Catalog

  7. Composition of Trig Functions and Inverses • Recall that in general • f-1(f(x)) = f(f-1(x)) = x • For trig functions this is the same • sin(arcsin(x)) = arcsin(sin(x)) • The restriction on the domain and range of the inverse functions must apply • Thus • sin-1(sin(3)) could not be 3 • Note calculator results

  8. Composition of Trig Functions and Inverses • Try these … with and without calculator

  9. Solving Inverse Trig Equations • Given • Strategy • Isolate the sin-1x • Take the sine of both sides of the equation

  10. Try it Out • Try this one

  11. Assignment • Lesson 3.5 • Page 265 • Exercises 1 – 65 EOO

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