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- Using an Inverse TrigonometricFunction In Exercises 39–44, use aninverse trigonometric function to write θ asa function of x.Calculators and Inverse Trigonometric Functions In Exercises 121-126, use the results of Exercises 111-113 and a calculator to approximate the value of the expression. Round your result to two decimal places. arccot5.25Inverse Trigonometric Functions Are the derivatives of the inverse trigonometric functions algebraic or transcendental functions? Explain.
- Verifying a Trigonometric IdentityIn Exercises 19–24, verify the identityalgebraically. Use the table feature ofa graphing utility to check your resultnumerically.Behavior of an Inverse Trigonometric FunctionIn Exercises 93–98, fill in the blank. If not possible, statethe reason. (Note: The notation x→c+ indicates that xapproaches c from the right and x→c− indicates that xapproaches c from the left.)93. As x→1−, the value of arcsin x→■.94. As x→1−, the value of arccos x→■.95. As x→∞, the value of arctan x→■.96. As x→−1+, the value of arcsin x→■.97. As x→−1+, the value of arccos x→■.98. As x→−∞, the value of arctan x→■.Evaluating an Inverse TrigonometricFunction In Exercises 77–80, find the exact value ofthe expression.77. arcsin(−1)78. cos−1 179. arccot √380. arcsec(−√2)
- Evaluating an Inverse TrigonometricFunction In Exercises 5–18, find the exactvalue of the expression, if possible.Using reciprocal identities how do you solve this problem? is it solvable? Cosx - Secx = -SinxTanxDeriving a Reduction Formula InExercises 65–68, write the expression as atrigonometric function of only θ, and usea graphing utility to confirm your answergraphically.
- 9. Inverse Trigonometric FunctionsIdentifying Damped Trigonometric FunctionsIn Exercises 65–68, match the function with its graph.Describe the behavior of the function as x approacheszero. [The graphs are labeled (a), (b), (c), and (d).]Summarize how the derivatives of inverse trigonometric functions are related to the derivatives of the corresponding inverse cofunctions (for example, inverse tangent and inverse cotangent).