chapter 1(2) - MATH1010U Chapter 1 cont 1 FUNCTIONS AND...

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MATH1010U: Chapter 1 cont… 1 FUNCTIONS AND MODELS cont… Inverse Functions and Logarithms (Section 1.6, pg. 63) cont… Recall: Last class, we reviewed the concept of inverse functions. Let’s now apply this knowledge to find the inverse trigonometric functions. Recall: sin 6 π = 2 1 So, what if you’re asked to solve sin 2 1 ) ( = x ? Notation: In the above example, we want = 2 1 sin 1 x . In Maple: > arcsin(1/2); To find an inverse, we must restrict the domain of the function to ensure that it’s one-to-one. 2 2 sin ) ( sin 1 = = y x y y x
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MATH1010U: Chapter 1 cont… 2 Application: A compound lens is made from crown glass ( n = 1.52) bonded to flint glass ( n = 1.89). What is the critical angle for light incident on the flint-crown interface? [Some physics background: Refraction is the bending of light at an interface between transparent mediums. Total internal reflection occurs when light propagating in a
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chapter 1(2) - MATH1010U Chapter 1 cont 1 FUNCTIONS AND...

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