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 . Calisia . McLean. Trigonomic functions. The trigonometric functions are among the most fundamental in mathematics. The significance of applied mathematics extends beyond basic uses, because they can be used to describe any natural phenomenon that is periodic, and in higher mathematics they are fundamental tools for understanding many abstract spaces.. . Relations. and . Functions. OBJ: . . . Find the . inverse. of a . relation. . . . . Draw the . graph. of a . function . and its . inverse. . . Determine whether the. 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. 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]. . We know how to graph the inverse of a function, but now we will look into expressing a new inverse function. Like before, let’s keep in mind the “switching x and y” theory. f. -1. (x). The inverse of the function f(x), f. We’ll do the same things today as yesterday but today instead of x as the variable, we’ll have trig functions as the variable. Always look for a GCF first!. Difference of Squares. Factoring Trinomials. Int. Math 2. Vocabulary. Linear, non-linear, increasing, decreasing, rate of change, growth rate, domain, range, continuous, discontinuous, discrete, relation, function, inverse function, inverse . of a . 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. 1. Recall: We’ve defined the sine function in two ways. :. . and. ..  . 2. All the trig functions can also be defined in terms of the . unit circle. (circle with radius 1, centered at the origin. 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 . For Dummies. K.  . Evaluating Trig Functions. Step 1. Find the reference angle and graph it. sin380°. Step one find reference angle and graph.. Take 380-360 to get 20° for reference angle and then step one is complete . Right Triangle Trigonometry. Essential Question – How can right triangles help solve real world applications?. The Pythagorean theorem. In a rt . Δ. the square of the length of the hypotenuse is equal to the sum of the squares of the lengths of the legs.. 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.