3. Unit Circle

Use a calculator to evaluate each expression. 2 sin 25°13' cos 25°13' - sin 50°26'

Find the exact value of s in the given interval that has the given circular function value.

[π, 3π/2] ; tan s = √3

On the unit circle, what relationship do the ratios $\frac{\sin x}{1}$ and $\frac{\cos y}{1}$ share for any real values of $x$ and $y$?

Find a calculator approximation to four decimal places for each circular function value.

sin 1.0472

Find a calculator approximation to four decimal places for each circular function value. See Example 3. tan 4.0203

Find all values of θ, if θ is in the interval [0°, 360°) and has the given function value. See Example 6. √3 sin θ = - —— 2

Without using a calculator, decide whether each function value is positive or negative. (Hint: Consider the radian measures of the quadrantal angles, and remember that π ≈ 3.14.)

tan 6.29

Find the approximate value of s, to four decimal places, in the interval [0, π/2] that makes each statement true.

sin s = 0.4924

Without using a calculator, decide whether each function value is positive or negative. (Hint: Consider the radian measures of the quadrantal angles, and remember that π ≈ 3.14.)

sin 5

Find all values of θ, if θ is in the interval [0°, 360°) and has the given function value. See Example 6. 1 cos θ = - — 2

Find each exact function value. See Example 2.

sec 23π/6

Determine whether each statement is true or false. If false, tell why. See Example 4. tan² 60° + 1 = sec² 60°

Use the formula ω = θ/t to find the value of the missing variable.

θ = 3.871 radians, t = 21.47 sec

Find the approximate value of s, to four decimal places, in the interval [0, π/2] that makes each statement true.

tan s = 0.2126

Find exact values of the six trigonometric functions for each angle. Do not use a calculator. Rationalize denominators when applicable. 120°