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Problem 1.RE.51
In Exercises 49–59, find the exact value of each expression. Do not use a calculator. sec 7𝜋 / 4
Problem 1.RE.54
In Exercises 49–59, find the exact value of each expression. Do not use a calculator. csc(-2𝜋/3)
Problem 1.RE.59
In Exercises 49–59, find the exact value of each expression. Do not use a calculator. cos(-35𝜋 / 6)
Problem 1.RE.49
In Exercises 49–59, find the exact value of each expression. Do not use a calculator. sin 240°
Problem 1.RE.55
In Exercises 49–59, find the exact value of each expression. Do not use a calculator. sin(-𝜋/3)
Problem 2
In Exercises 2–4, convert each angle in degrees to radians. Express your answer as a multiple of 𝜋. 15°
Problem 4
In Exercises 2–4, convert each angle in degrees to radians. Express your answer as a multiple of 𝜋. 315°
Problem 5
In Exercises 5–7, convert each angle in radians to degrees. 5𝜋 3
Problem 6
In Exercises 5–7, convert each angle in radians to degrees. 7𝜋 5
Problem 7
In Exercises 5–7, convert each angle in radians to degrees. - 5𝜋 6
Problem 8
In Exercises 8–12, draw each angle in standard position. 5𝜋 6
Problem 10
In Exercises 8–12, draw each angle in standard position. 8𝜋 3
Problem 12
In Exercises 8–12, draw each angle in standard position. -135°
Problem 14
In Exercises 13–17, find a positive angle less than 360° or 2𝜋 that is coterminal with the given angle. -445°
Problem 27
If θ is an acute angle and sin θ = (2√7) / 7, use the identity sin²θ + cos²θ = 1 to find cos θ.
Problem 28
In Exercises 28–29, find a cofunction with the same value as the given expression. sin 70°
Problem 29
Find a cofunction with the same value as the given expression.
cos (𝜋/2)
Problem 30
In Exercises 30–32, find the measure of the side of the right triangle whose length is designated by a lowercase letter. Round answers to the nearest whole number.
Problem 38
In Exercises 37–38, a point on the terminal side of angle θ is given. Find the exact value of each of the six trigonometric functions of θ, or state that the function is undefined.
(0, -1)
Problem 39
In Exercises 39–40, let θ be an angle in standard position. Name the quadrant in which θ lies.
tan θ > 0 and sec θ > 0
Problem 40
In Exercises 39–40, let θ be an angle in standard position. Name the quadrant in which θ lies.
tan θ > 0 and cos θ < 0
Problem 41
In Exercises 41–43, find the exact value of each of the remaining trigonometric functions of θ.
cos θ = 2/5, sin θ < 0
Problem 44
In Exercises 44–48, find the reference angle for each angle.
265°
Problem 46
In Exercises 44–48, find the reference angle for each angle.
-410°
Problem 48
In Exercises 44–48, find the reference angle for each angle.
- 11𝜋/3
Problem 1
Convert 135° to an exact radian measure.
Problem 2
Find the length of the arc on a circle of radius 20 feet intercepted by a 75° central angle. Express arc length in terms of 𝜋. Then round your answer to two decimal places.
Problem 4a
Find a positive angle less than 2𝜋 that is coterminal with 16𝜋 3
Problem 4b
Find the reference angle for 16𝜋 3
Problem 9
In Exercises 8–13, find the exact value of each expression. Do not use a calculator. tan 300°