PPT-5.8 Inverse Trig Functions

Definition of Inverse Trig Functions Graphs of inverse functions Page 381 Ex 1 Evaluating Inverse Trig Functions a arcsin 12 b arcsin 03 Properties of Inverse Functions If 1x1 and . Another natural way to define relations is to define both elements of the ordered pair (x, y), in terms of another variable . t. , called a . parameter. Parametric equations: . equations in the form. Section 6.3 Beginning on page 310. Logarithms. For what value of x does . ? Logarithms can answer this question. Log is the inverse operation to undo unknown exponents. .  .  .  .  .  . *Read as log base b of y. Agenda. Do Now. Quiz Review. Lesson 26 #1-4. Trigonometric Ratios. Fisher Building Problem. Debrief. DO NOW 1/5:. Label the opposite, adjacent and hypotenuse for reference angle A.. θ. Quiz Review. Lesson 26: Classwork #1-3. Verifying trig identities algebraically involves . transforming one side . of the equation into the same form as the other side using basic trig identities and properties of algebra. . Procedure for Verifying Trig Identities. Enea. Sacco. 2. Welcome to Calculus I!. Welcome to Calculus I. 3. Topics/Contents . Before Calculus. Functions. New functions from the old. Inverse Functions. Trigonometric Functions. Inverse Trigonometric Functions. Exponential and Logarithmic Functions. A bit more practice in Section 4.7b. Analysis of the Inverse Sine Function. 1. –1. D:. R:. Continuous. Increasing. Symmetry: Origin (odd . func. .). Bounded. Abs. Max. of at . x. = 1. Abs. Min. of at . 2.2 trig ratios with obtuse angles. Trig ratios with obtuse angles. “OBTUSE”. : Greater than 90. o. , less than 180. o. Similarly, coordinates on a . Cartesian Plane. are used to determine a location on a plane relative to the origin. Section 5.6 Beginning on Page 276. What is the Inverse of a Function?. The inverse of a function is a generic equation to find the input of the original function when given the output [finding x when given y]. . Some needed trig identities:. Trig Derivatives. Graph . y. 1. = sin x. . and . y. 2. = . nderiv. (sin x). What do you notice?. Proof Algebraically. (use trig identity for . sin(x + h). ). Proof Algebraically. The . inverse . of a relation is the set of ordered pairs obtained by . switching the input with the output. of each ordered pair in the original relation. (The domain of the original is the range of the inverse; and vice versa). A function maps each element in the domain to exactly 1 element in the range. . Concept 1. Example 1. Domain and Range. State the domain and range of the relation. Then determine whether the relation is a function. If it is a function, determine if it is . Use the triangle given to find the following trig ratios. sin( θ ) cos ( θ ) tan( θ ) Solve for x in the proportions below. 5.   Warm Up 1/20 Get out a colored pen and last night’s homework p. 147. Product Rule.  . Quotient Rule. Derivatives of Trig Functions. More Derivatives of Trig Functions. Higher Order Derivatives. Also…. Homework. p. 154. 1. -57 EO odd. , . 65, 71,. 79, . 81, 88. Page: . 108. Inverse:. The reversal of some process or operation.. For functions, the reversal involves the interchange of the domain. with the range.. Along with the reversal of the domain and range there is a reversal.