In Exercises 55–58, use a calculator to find the value of the acute angle θ to the nearest degree. tan θ = 4.6252

In Exercises 5–18, the unit circle has been divided into twelve equal arcs, corresponding to t-values of

0, 𝜋, 𝜋, 𝜋, 2𝜋, 5𝜋, 𝜋, 7𝜋, 4𝜋, 3𝜋, 5𝜋, 11𝜋, and 2𝜋.

6 3 2 3 6 6 3 2 3 6

Use the (x,y) coordinates in the figure to find the value of each trigonometric function at the indicated real number, t, or state that the expression is undefined.

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In Exercises 11–18, continue to refer to the figure at the bottom of the previous page.

sec 3𝜋/2

Find a cofunction with the same value as the given expression.

cos (𝜋/2)

A point P(x, y) is shown on the unit circle corresponding to a real number t. Find the values of the trigonometric functions at t.

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In Exercises 59–62, use a calculator to find the value of the acute angle θ in radians, rounded to three decimal places. cos θ = 0.4112

In Exercises 41–56, use the circle shown in the rectangular coordinate system to draw each angle in standard position. State the quadrant in which the angle lies. When an angle's measure is given in radians, work the exercise without converting to degrees.

-210°

In Exercises 57–70, find a positive angle less than or that is coterminal with the given angle. 17𝜋 /5

In Exercises 63–68, find the exact value of each expression. Do not use a calculator. tan(𝜋/3)/2 - 1/sec(𝜋/6)

If θ is an acute angle and cos θ = 1/3, find csc (𝜋/2 - θ).

In Exercises 1–8, a point on the terminal side of angle θ is given. Find the exact value of each of the six trigonometric functions of θ. (-4, 3)

In Exercises 57–70, find a positive angle less than or that is coterminal with the given angle. -150°

In Exercises 71–74, find the length of the arc on a circle of radius r intercepted by a central angle θ. Express arc length in terms of 𝜋. Then round your answer to two decimal places. Radius, r: 8 feet Central Angle, θ: θ = 225°

In Exercises 57–70, find a positive angle less than or that is coterminal with the given angle. - 38𝜋/9

In Exercises 55–58, use a calculator to find the value of the acute angle θ to the nearest degree. sin θ = 0.2974

In Exercises 41–56, use the circle shown in the rectangular coordinate system to draw each angle in standard position. State the quadrant in which the angle lies. When an angle's measure is given in radians, work the exercise without converting to degrees.

120°

In Exercises 63–68, find the exact value of each expression. Do not use a calculator. cos 12° sin 78° + cos 78° sin 12°

In Exercises 61–86, use reference angles to find the exact value of each expression. Do not use a calculator. tan(-𝜋/4)

In Exercises 61–86, use reference angles to find the exact value of each expression. Do not use a calculator. sin(-240°)

In Exercises 57–70, find a positive angle less than or that is coterminal with the given angle. 395°

In Exercises 57–70, find a positive angle less than or that is coterminal with the given angle. 25𝜋 6

In Exercises 61–86, use reference angles to find the exact value of each expression. Do not use a calculator. sin(2𝜋/3)

In Exercises 41–56, use the circle shown in the rectangular coordinate system to draw each angle in standard position. State the quadrant in which the angle lies. When an angle's measure is given in radians, work the exercise without converting to degrees.

14𝜋/3

In Exercises 63–68, find the exact value of each expression. Do not use a calculator. 1 + sin² 40° + sin² 50°

In Exercises 35–60, find the reference angle for each angle. - 11𝜋 / 4

In Exercises 35–60, find the reference angle for each angle. -13𝜋/3

In Exercises 61–86, use reference angles to find the exact value of each expression. Do not use a calculator. cos 225°

In Exercises 71–74, find the length of the arc on a circle of radius r intercepted by a central angle θ. Express arc length in terms of 𝜋. Then round your answer to two decimal places. Radius, r: 12 inches Central Angle, θ: θ = 45°

In Exercises 35–60, find the reference angle for each angle. 17𝜋 / 6

In Exercises 57–70, find a positive angle less than or that is coterminal with the given angle. -760°

In Exercises 59–62, use a calculator to find the value of the acute angle θ in radians, rounded to three decimal places. tan θ = 0.4169