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.

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.

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

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

sin (2π − x)

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)

Which of the following is the period of the function $z=\sin (x-y)$ with respect to $x$?

57. Explain why or why not Determine whether the following statements are true and give an explanation or counterexample.

a. If x = 4 tanθ, then cscθ = 4/x.