Convert the angle $-\frac{5\pi}{6}$ from radians to degrees.

A weight is attached to a spring and reaches its equilibrium position (x = 0). It is then set in motion resulting in a displacement of x = 10 cos t, where x is measured in centimeters and t is measured in seconds. See the accompanying figure.

Find the spring’s displacement when t = 0, t = π/3, and t = 3π/4.

Assume that a particle’s position on the x-axis is given by

x = 3 cos t + 4 sin t,

where x is measured in feet and t is measured in seconds.

a. Find the particle’s position when t = 0, t = π/2, and t = π.

Computer Explorations

Use a CAS to perform the following steps in Exercises 55–62.

a. Plot the equation with the implicit plotter of a CAS. Check to see that the given point P satisfies the equation.

xy³ + tan(x + y) = 1, P(π/4, 0)

Convert the angle $540°$ from degrees to radians.

Given the right triangle below, evaluate $\cos\theta$.

Given the right triangle below, evaluate $\tan\theta$.

Identify what angle, $\theta$ , satisfies the following conditions.

$\sin\theta=\frac12$; $\tan\theta$ < $0$

Identify what angle, $\theta$ , satisfies the following conditions.

$\cos\theta=\frac{\sqrt3}{2}$; $\sin\theta$ < $0$