Chapter 14

Evaluate to four significant digits. $$\arccos 0.6243$$

Evaluate to four significant digits. $$\cos ^{-1} 0.2320$$

Evaluate to four significant digits. $$\operatorname{arccot} 1.546$$

Evaluate to four significant digits. $$\sin ^{-1} 0.2649$$

Evaluate to four significant digits. $$\csc ^{-1} 2.6263$$

Evaluate to four significant digits. $$\arctan 3.7253$$

Evaluate to four significant digits. $$\operatorname{arcsec} 2.8463$$

Evaluate to four significant digits. $$\sin ^{2} \frac{\pi}{6}+\cos \frac{\pi}{6}$$

Evaluate to four significant digits. $$7 \tan ^{2} \frac{\pi}{9}$$

Evaluate to four significant digits. $$\cos ^{2} \frac{3 \pi}{4}$$

Evaluate to four significant digits. $$\frac{\pi}{6} \sin \frac{\pi}{6}$$

Evaluate to four significant digits. $$\sin \frac{\pi}{8} \tan \frac{\pi}{8}$$

Evaluate to four significant digits. $$3 \sin \frac{\pi}{9} \cos ^{2} \frac{\pi}{9}$$

Find the area of a sector having a radius of 5.92 in. and a central angle of \(62.5^{\circ} .\)

Find the area of a sector having a radius of \(3.15 \mathrm{m}\) and a central angle of \(28.3^{\circ} .\)

A weight bouncing on the end of a spring moves with simple harmonic motion according to the equation \(y=4 \cos 25 t,\) where \(y\) is in inches. Find the displacement \(y\) when \(t=2.00 \mathrm{s}\). (In this equation, the angle \(25 t\) must be in radians.)

For the angles from \(0^{\circ}\) to \(10^{\circ}\), with steps every \(1 / 2^{\circ}\) use a spreadsheet to compute and print each angle in radians, and the sine and tangent of that angle, to four decimal places. What do you notice about these three columns of figures? What is the largest angle for which the sine and tangent do not differ from the angle itself by more than three significant digits? How could you use this information?