Evaluate the expression.
$\cos^{-1}\left(-1\right)$

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.)

An inverse tangent identity

b. Prove that tan⁻¹ x + tan⁻¹ x(1/x) = π/2, for x > 0.

Verify the identity sec⁻¹ x = cos⁻¹ (1/x), for x ≠ 0.

Evaluate the expression.

$\cos^{-1}\left(0\right)$

Evaluate the expression.

$\cos^{-1}\left(-\frac{\sqrt2}{2}\right)$

Evaluate the expression.

$\sin^{-1}1$

Evaluate the expression.

$\sin^{-1}\left(\frac{\sqrt3}{2}\right)$