0. Functions

Evaluate the expression.

$\cos^{-1}\left(\cos\left(\frac{\pi}{2}\right)\right)$

Evaluate the expression.

$\tan^{-1}\left(\tan\frac{2\pi}{3}\right)$

Evaluating inverse trigonometric functions Without using a calculator, evaluate the following expressions.

$\csc^{-1}\left(-1\right)$

Evaluating inverse trigonometric functions Without using a calculator, evaluate the following expressions.

$\tan^{-1}\left(\tan\left(\frac{\pi}{4}\right)\right)$

Evaluating inverse trigonometric functions Without using a calculator, evaluate the following expressions.

$\tan^{-1}\left(\tan\left(\frac{3\pi}{4}\right)\right)$

Evaluating inverse trigonometric functions Without using a calculator, evaluate the following expressions.

$\tan\left(\tan^{-1}1\right)$

Express $\theta$ in terms of $x$ using the inverse sine, inverse tangent, and inverse secant functions. <IMAGE>

Evaluating inverse trigonometric functions Without using a calculator, evaluate the following expressions.

$\tan^{-1}\sqrt3$

Inverse sines and cosines Evaluate or simplify the following expressions without using a calculator.

cos⁻¹ √3/2

Inverse sines and cosines Evaluate or simplify the following expressions without using a calculator.

cos⁻¹ (- 1/2 )

Inverse sines and cosines Evaluate or simplify the following expressions without using a calculator.

sin⁻¹ ( -1 )

Inverse sines and cosines Evaluate or simplify the following expressions without using a calculator.

cos (cos⁻¹ ( -1 ))

62–65. {Use of Tech} Graphing f and f'

a. Graph f with a graphing utility.

f(x) = (x−1) sin^−1 x on [−1,1]

62–65. {Use of Tech} Graphing f and f'

a. Graph f with a graphing utility.

f(x)=e^−x tan^−1 x on [0,∞)

Tracking a dive A biologist standing at the bottom of an 80-foot vertical cliff watches a peregrine falcon dive from the top of the cliff at a 45° angle from the horizontal (see figure). <IMAGE>

a. Express the angle of elevation θ from the biologist to the falcon as a function of the height h of the bird above the ground. (Hint: The vertical distance between the top of the cliff and the falcon is 80−h.)