Refer to the given figure. Write the radius r of the circle in terms of α and θ.

Evaluating trigonometric functions Without using a calculator, evaluate the following expressions or state that the quantity is undefined.

sec (5π/2)

[Technology Exercise]

You want to make an 80° angle by marking an arc on the perimeter of a 12-in.-diameter disk and drawing lines from the ends of the arc to the disk’s center. To the nearest tenth of an inch, how long should the arc be?

Radians and Degrees

On a circle of radius 10 m, how long is an arc that subtends a central angle of (a) 4π/5 radians? (b) 110°?

Copy and complete the following table of function values. If the function is undefined at a given angle, enter “UND.” Do not use a calculator or tables.

In Exercises 39–42, express the given quantity in terms of sin x and cos x.

sin (2π − x)

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)