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Problem 1.3.59
Find the reference angle for each angle.
-25π/6
Problem 1.3.52
In Exercises 35–60, find the reference angle for each angle. 553°
Problem 1.3.67
In Exercises 61–86, use reference angles to find the exact value of each expression. Do not use a calculator. sin(2𝜋/3)
Problem 1.3.73
In Exercises 61–86, use reference angles to find the exact value of each expression. Do not use a calculator. sin(-240°)
Problem 1
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)
Problem 1.3.61
In Exercises 61–86, use reference angles to find the exact value of each expression. Do not use a calculator. cos 225°
Problem 1.3.72
In Exercises 61–86, use reference angles to find the exact value of each expression. Do not use a calculator. tan(9𝜋/2)
Problem 4
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. (3, 7)
Problem 6
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. (5, -5)
Problem 8
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. (-1, -3)
Problem 10
In Exercises 9–16, evaluate the trigonometric function at the quadrantal angle, or state that the expression is undefined. tan 𝜋
Problem 12
In Exercises 9–16, evaluate the trigonometric function at the quadrantal angle, or state that the expression is undefined. csc 𝜋
Problem 27
In Exercises 23–34, find the exact value of each of the remaining trigonometric functions of θ. cos θ = 8/17, 270° < θ < 360°
Problem 29
In Exercises 23–34, find the exact value of each of the remaining trigonometric functions of θ. tan θ = -2/3, sin θ > 0
Problem 31
In Exercises 23–34, find the exact value of each of the remaining trigonometric functions of θ. tan θ = 4/3, cos θ < 0
Problem 33
In Exercises 23–34, find the exact value of each of the remaining trigonometric functions of θ. sec θ = -3, tan θ > 0
Problem 35
In Exercises 35–60, find the reference angle for each angle. 160°
Problem 37
Find the reference angle for each angle.
205°
Problem 39
In Exercises 35–60, find the reference angle for each angle.
355°
Problem 41
In Exercises 35–60, find the reference angle for each angle.
7𝜋/4
Problem 42
Find the reference angle for each angle.
5π/4
Problem 45
In Exercises 35–60, find the reference angle for each angle.
-150°
Problem 77
Use reference angles to find the exact value of each expression. Do not use a calculator. sec 495°
Problem 77
Find the area of the sector of a circle of radius r formed by a central angle θ. Express area in terms of π. Then round your answer to two decimal places. Radius, r: 4 inches Central Angle, θ: θ = 240°
Problem 79
Use reference angles to find the exact value of each expression. Do not use a calculator. cot 19𝜋/6
Problem 83
In Exercises 61–86, use reference angles to find the exact value of each expression. Do not use a calculator. tan (-17𝜋/6)
Problem 84
Use the circle shown in the rectangular coordinate system to solve Exercises 81–86. Find two angles, in radians, between -2𝜋 and 2𝜋 such that each angle's terminal side passes through the origin and the given point.
F
Problem 85
Use reference angles to find the exact value of each expression. Do not use a calculator. sin (-17𝜋/3)
Problem 87
In Exercises 87–92, find the exact value of each expression. Write the answer as a single fraction. Do not use a calculator. sin 𝜋/3 cos 𝜋 - cos 𝜋/3 sin 3𝜋/2
Problem 91
Find the exact value of each expression. Write the answer as a single fraction. Do not use a calculator. sin (3𝜋/2) tan (-15𝜋/4) - cos (-5𝜋/3)
