Consider the inverse tangent function y = tan-1 x, or y = arctan x. (a) What is its domain? (b) What is its range? (c) Is this function increasing or decreasing? (d) Is there any real number x for which arctan x is not defned? If so, what is it (or what are they)?

Express the following function as a purely algebraic function. Answer sin (cos-¹ (²-)) sin (cos-¹(²)) = Keypad Keyboard Shortcuts

Find the value of the function if it is defined. If it is not defined, enter DNE in the answer blank to receive credit. For part (a) give the exact value if it exists. For part (b) you may need a calculator; in that case give the answer to three decimal places. (a) sec (cos1 (-1)) = (b) sin-1 (cos (1.1)) =

The actual temperature inside an oven varies around the selected temperature. This variation can be modeled with a sine function. If the cook selected a temperature of 425 °F, then the actual temperature T in the oven is given by T = 20 sin(2x) + 425, where it is the number of hours since the oven first hit the selected temperature of 425°F. What is the highest actual temperature in the oven? 'F What is the lowest actual temperature in the oven? What is the period of this function? Give your answer in minutes. minutes When is the first time the oven will hit the highest temperature? Give your answer in minutes. minutes

Use the trigonometric substitution to select the algebraic expression as a trigonometric function of theta, where 0< θ<π/2 √4-x^2, x=2cosθ a. 4cosθ b. 2cosθ c. 2sinθ d. 4sinθ e. -2sinθ

Explain how the graph of r(x)=-3tan(1/2x) is related to the graph of the basic trigonometric function f(x)=tanx Part I: What kind of reflection does the basic function experience? Part II: What is the vertical stretch factor of the function R(x)? Vertical shift ; none Part III: What is the horizontal stretch factor of the function R(x)?

In a certain piston engine, the distance x (in centimeters) from the center of the drive shaft to head of piston is given by the function (Function is in the image provided) Where (theta) is an angle in degrees between the crank and the path of the piston head. Find x when (theta) = 30(degrees) and when (theta) = 45(degrees) round answer to the nearest thousandth centimeter.

4) Let the function f be defined as f(x) = sin(x) for all x. An example visualization is shown in the graph below. Sine Wave MA Time Investopedia a. What is the domain and co-domain? Be explicit when it comes to defining the range of values for both. b. Based on your answers for the previous question (a), is the function one-to-one? Is it onto? Explain your reasoning. Amplitude