please do the following problems and show the work

Derivatives of Inverse Trigonometric Functions EU. {a} Give three different domain intervals of length n" where the sine function is one- to-one- {h} Sketch a graph of y = sins" on the restricted domain |%_.%]. Give the range in interval notation. {c} Dene the inverse sine [arcsine] function by writing y = arcsina' if and only if :r = siny, where y E [%,%] and s' E [111]. Sketch a graph of the arcsine function- Give the domain and range of the arcsine function. How is this graph related to the graph of the sine? 31. Let y = arcsinzr. {a} Solve for a. {h} Take the derivative of both sides of your equation from part [a]. Employ the chain rule every time you need to apply the i to a y-variahle. fly [c]I Solve for . Use your equation from part [a] to write your answer as a function tin: of :r. {:1} Use your result to complete the following Theorem. Theorem 39 [Derivative of the Inverse Sine} d arcsin :r = it 32. {a} Sketch a graph of y = tan: on the restricted domain {g, g]. Give the range in interval notation. {h} Define the inverse tangent [arctangent]I function by writing y = arctanJ: if and only if a = tan y where y E {%J%]_ Sketch a graph of the arctangent function. Give the domain and range of the arctangent function- Hov.r is this graph related to the graph of the tangent