A) Sketch the reference angle for θ = 5π/4 in the correct quadrant. B) Find sin θ, cos θ, tan θ, csc θ, sec θ, & cot θ,

sin(5π/4) = -√2/2, cos(5π/4) = -√2/2, tan(5π/4) = 1, csc(5π/4) = -√2, sec(5π/4) = -√2, cot(5π/4) = 1

sin(5π/4) = √2/2, cos(5π/4) = -√2/2, tan(5π/4) = -1, csc(5π/4) = √2, sec(5π/4) = -√2, cot(5π/4) = -1

sin(5π/4) = -√2/2, cos(5π/4) = √2/2, tan(5π/4) = -1, csc(5π/4) = -√2, sec(5π/4) = √2, cot(5π/4) = -1

sin(5π/4) = -1, cos(5π/4) = 0, tan(5π/4) = undefined, csc(5π/4) = -1, sec(5π/4) = undefined, cot(5π/4) = 0

A) Sketch the reference angle for θ = π/3 in the correct quadrant. B) Find sin θ, cos θ, tan θ, csc θ, sec θ, & cot θ, Fill in the blanks with the correct values.

sin(π/3) = √3/2, cos(π/3) = 1/2, tan(π/3) = √3, csc(π/3) = 2/√3, sec(π/3) = 2, cot(π/3) = 1/√3

sin(π/3) = 1/2, cos(π/3) = √3/2, tan(π/3) = 1/√3, csc(π/3) = 2, sec(π/3) = 2/√3, cot(π/3) = √3

sin(π/3) = -√3/2, cos(π/3) = -1/2, tan(π/3) = √3, csc(π/3) = -2/√3, sec(π/3) = -2, cot(π/3) = 1/√3

sin(π/3) = -1/2, cos(π/3) = √3/2, tan(π/3) = -1/√3, csc(π/3) = -2, sec(π/3) = 2/√3, cot(π/3) = -√3

A) Sketch the reference angle for θ = 5π/6 in the correct quadrant. B) Find sin θ, cos θ, tan θ, csc θ, sec θ, & cot θ, Fill in the blanks with the correct values.

sin(5π/6) = 1/2, cos(5π/6) = -√3/2, tan(5π/6) = -1/√3, csc(5π/6) = 2, sec(5π/6) = -2/√3, cot(5π/6) = -√3

sin(5π/6) = -1/2, cos(5π/6) = √3/2, tan(5π/6) = 1/√3, csc(5π/6) = -2, sec(5π/6) = 2/√3, cot(5π/6) = √3

sin(5π/6) = -1/2, cos(5π/6) = -√3/2, tan(5π/6) = 1/√3, csc(5π/6) = -2, sec(5π/6) = -2/√3, cot(5π/6) = √3

sin(5π/6) = 1/2, cos(5π/6) = √3/2, tan(5π/6) = 1/√3, csc(5π/6) = 2, sec(5π/6) = 2/√3, cot(5π/6) = √3

A) Sketch the reference angle for θ = π/4 in the correct quadrant. B) Find sin θ, cos θ, tan θ, csc θ, sec θ, & cot θ, Fill in the blanks with the correct values.

sin(π/4) = √2/2, cos(π/4) = √2/2, tan(π/4) = 1, csc(π/4) = √2, sec(π/4) = √2, cot(π/4) = 1

sin(π/4) = 1/2, cos(π/4) = √3/2, tan(π/4) = √3, csc(π/4) = 2, sec(π/4) = 2/√3, cot(π/4) = 1/√3

sin(π/4) = -√2/2, cos(π/4) = -√2/2, tan(π/4) = 1, csc(π/4) = -√2, sec(π/4) = -√2, cot(π/4) = 1

sin(π/4) = -1/2, cos(π/4) = √3/2, tan(π/4) = -√3, csc(π/4) = -2, sec(π/4) = 2/√3, cot(π/4) = -1/√3

A) Sketch the reference angle for θ = 5π/3 in the correct quadrant. B) Find sin θ, cos θ, tan θ, csc θ, sec θ, & cot θ. Fill in the blanks with the correct values.

sin(5π/3) = -√3/2, cos(5π/3) = 1/2, tan(5π/3) = -√3, csc(5π/3) = -2/√3, sec(5π/3) = 2, cot(5π/3) = -1/√3

sin(5π/3) = √3/2, cos(5π/3) = -1/2, tan(5π/3) = -√3, csc(5π/3) = 2/√3, sec(5π/3) = -2, cot(5π/3) = -1/√3

sin(5π/3) = √3/2, cos(5π/3) = 1/2, tan(5π/3) = √3, csc(5π/3) = 2/√3, sec(5π/3) = 2, cot(5π/3) = 1/√3

sin(5π/3) = -1/2, cos(5π/3) = √3/2, tan(5π/3) = -1/√3, csc(5π/3) = -2, sec(5π/3) = 2/√3, cot(5π/3) = -√3

A) Sketch the reference angle for θ = 13π/6 in the correct quadrant. B) Find sin θ, cos θ, tan θ, csc θ, sec θ, & cot θ,

sin(13π/6) = 1/2, cos(13π/6) = √3/2, tan(13π/6) = 1/√3, csc(13π/6) = 2, sec(13π/6) = 2/√3, cot(13π/6) = √3

sin(13π/6) = -1/2, cos(13π/6) = √3/2, tan(13π/6) = -1/√3, csc(13π/6) = -2, sec(13π/6) = 2/√3, cot(13π/6) = -√3

sin(13π/6) = 1/2, cos(13π/6) = -√3/2, tan(13π/6) = -1/√3, csc(13π/6) = 2, sec(13π/6) = -2/√3, cot(13π/6) = -√3

sin(13π/6) = -1/2, cos(13π/6) = -√3/2, tan(13π/6) = 1/√3, csc(13π/6) = -2, sec(13π/6) = -2/√3, cot(13π/6) = √3

A) Sketch the reference angle for θ = -π/6 in the correct quadrant. B) Find sin θ, cos θ, tan θ, csc θ, sec θ, & cot θ. Fill in the blanks with the correct values.

sin(-π/6) = -1/2, cos(-π/6) = √3/2, tan(-π/6) = -1/√3, csc(-π/6) = -2, sec(-π/6) = 2/√3, cot(-π/6) = -√3

sin(-π/6) = 1/2, cos(-π/6) = -√3/2, tan(-π/6) = 1/√3, csc(-π/6) = 2, sec(-π/6) = -2/√3, cot(-π/6) = √3

sin(-π/6) = -√3/2, cos(-π/6) = 1/2, tan(-π/6) = -√3, csc(-π/6) = -2/√3, sec(-π/6) = 2, cot(-π/6) = -1/√3

sin(-π/6) = 1/2, cos(-π/6) = √3/2, tan(-π/6) = 1/√3, csc(-π/6) = 2, sec(-π/6) = 2/√3, cot(-π/6) = √3

A) Sketch the reference angle for θ = -2π/3 in the correct quadrant. B) Find sin θ, cos θ, tan θ, csc θ, sec θ, & cot θ. Fill in the blanks with the correct values.

sin(-2π/3) = -√3/2, cos(-2π/3) = -1/2, tan(-2π/3) = √3, csc(-2π/3) = -2/√3, sec(-2π/3) = -2, cot(-2π/3) = 1/√3

sin(-2π/3) = 1/2, cos(-2π/3) = √3/2, tan(-2π/3) = 1/√3, csc(-2π/3) = 2, sec(-2π/3) = 2/√3, cot(-2π/3) = √3

sin(-2π/3) = √3/2, cos(-2π/3) = -1/2, tan(-2π/3) = -√3, csc(-2π/3) = 2/√3, sec(-2π/3) = -2, cot(-2π/3) = -1/√3

sin(-2π/3) = -1, cos(-2π/3) = 0, tan(-2π/3) = undefined, csc(-2π/3) = undefined, sec(-2π/3) = undefined, cot(-2π/3) = 0

A) Sketch the reference angle for θ = -5π/4 in the correct quadrant. B) Find sin θ, cos θ, tan θ, csc θ, sec θ, & cot θ,

sin(-5π/4) = -√2/2, cos(-5π/4) = -√2/2, tan(-5π/4) = 1, csc(-5π/4) = -√2, sec(-5π/4) = -√2, cot(-5π/4) = 1

sin(-5π/4) = √2/2, cos(-5π/4) = -√2/2, tan(-5π/4) = -1, csc(-5π/4) = √2, sec(-5π/4) = -√2, cot(-5π/4) = -1

sin(-5π/4) = -1, cos(-5π/4) = 0, tan(-5π/4) = undefined, csc(-5π/4) = undefined, sec(-5π/4) = undefined, cot(-5π/4) = 0

sin(-5π/4) = √2/2, cos(-5π/4) = √2/2, tan(-5π/4) = 1, csc(-5π/4) = √2, sec(-5π/4) = √2, cot(-5π/4) = 1

A) Sketch the reference angle for θ = 2π/3 in the correct quadrant. B) Find sin θ, cos θ, tan θ, csc θ, sec θ, & cot θ. Fill in the blanks with the correct values.

sin(2π/3) = √3/2, cos(2π/3) = -1/2, tan(2π/3) = -√3, csc(2π/3) = 2/√3, sec(2π/3) = -2, cot(2π/3) = -1/√3

sin(2π/3) = 1/2, cos(2π/3) = √3/2, tan(2π/3) = √3, csc(2π/3) = 2, sec(2π/3) = 2/√3, cot(2π/3) = 1/√3

sin(2π/3) = -√3/2, cos(2π/3) = -1/2, tan(2π/3) = √3, csc(2π/3) = -2/√3, sec(2π/3) = -2, cot(2π/3) = 1/√3

sin(2π/3) = 1/2, cos(2π/3) = -√3/2, tan(2π/3) = -1/√3, csc(2π/3) = 2, sec(2π/3) = -2/√3, cot(2π/3) = -√3

A) Sketch the reference angle for θ = 7π/4 in the correct quadrant. B) Find sin θ, cos θ, tan θ, csc θ, sec θ, & cot θ, Fill in the blanks with the correct values.

sin(7π/4) = -√2/2, cos(7π/4) = √2/2, tan(7π/4) = -1, csc(7π/4) = -√2, sec(7π/4) = √2, cot(7π/4) = -1

sin(7π/4) = √2/2, cos(7π/4) = -√2/2, tan(7π/4) = 1, csc(7π/4) = √2, sec(7π/4) = -√2, cot(7π/4) = 1

sin(7π/4) = √2/2, cos(7π/4) = √2/2, tan(7π/4) = 1, csc(7π/4) = √2, sec(7π/4) = √2, cot(7π/4) = 1

sin(7π/4) = -1, cos(7π/4) = 0, tan(7π/4) = undefined, csc(7π/4) = -1, sec(7π/4) = undefined, cot(7π/4) = 0

A) Sketch the reference angle for θ = 11π/6 in the correct quadrant. B) Find sin θ, cos θ, tan θ, csc θ, sec θ, & cot θ. Fill in the blanks with the correct values.

sin(11π/6) = -1/2, cos(11π/6) = √3/2, tan(11π/6) = -1/√3, csc(11π/6) = -2, sec(11π/6) = 2/√3, cot(11π/6) = -√3

sin(11π/6) = 1/2, cos(11π/6) = √3/2, tan(11π/6) = 1/√3, csc(11π/6) = 2, sec(11π/6) = 2/√3, cot(11π/6) = √3

sin(11π/6) = -1/2, cos(11π/6) = -√3/2, tan(11π/6) = 1/√3, csc(11π/6) = -2, sec(11π/6) = -2/√3, cot(11π/6) = √3

sin(11π/6) = 1/2, cos(11π/6) = -√3/2, tan(11π/6) = -1/√3, csc(11π/6) = 2, sec(11π/6) = -2/√3, cot(11π/6) = -√3

A) Sketch each angle. B) Find sin θ, cos θ, tan θ, csc θ, sec θ, & cot θ. 25. θ = 3π/2

sin(3π/2) = -1, cos(3π/2) = 0, tan(3π/2) = undefined, csc(3π/2) = -1, sec(3π/2) = undefined, cot(3π/2) = 0

sin(3π/2) = 0, cos(3π/2) = -1, tan(3π/2) = 0, csc(3π/2) = undefined, sec(3π/2) = -1, cot(3π/2) = undefined

sin(3π/2) = 1, cos(3π/2) = 0, tan(3π/2) = undefined, csc(3π/2) = 1, sec(3π/2) = undefined, cot(3π/2) = 0

sin(3π/2) = 0, cos(3π/2) = 1, tan(3π/2) = 0, csc(3π/2) = undefined, sec(3π/2) = 1, cot(3π/2) = undefined

A) Sketch each angle. B) Find sin θ, cos θ, tan θ, csc θ, sec θ, & cot θ. 26. θ = 3π

sin(3π) = 0, cos(3π) = -1, tan(3π) = 0, csc(3π) = undefined, sec(3π) = -1, cot(3π) = undefined

sin(3π) = 1, cos(3π) = 0, tan(3π) = undefined, csc(3π) = 1, sec(3π) = undefined, cot(3π) = 0

sin(3π) = -1, cos(3π) = 0, tan(3π) = undefined, csc(3π) = -1, sec(3π) = undefined, cot(3π) = 0

sin(3π) = 0, cos(3π) = 1, tan(3π) = 0, csc(3π) = undefined, sec(3π) = 1, cot(3π) = undefined

A) Sketch each angle. B) Find sin θ, cos θ, tan θ, csc θ, sec θ, & cot θ. 27. θ = 5π/2

sin(5π/2) = 1, cos(5π/2) = 0, tan(5π/2) = undefined, csc(5π/2) = 1, sec(5π/2) = undefined, cot(5π/2) = 0

sin(5π/2) = 0, cos(5π/2) = 1, tan(5π/2) = 0, csc(5π/2) = undefined, sec(5π/2) = 1, cot(5π/2) = undefined

sin(5π/2) = -1, cos(5π/2) = 0, tan(5π/2) = undefined, csc(5π/2) = -1, sec(5π/2) = undefined, cot(5π/2) = 0

sin(5π/2) = 0, cos(5π/2) = -1, tan(5π/2) = 0, csc(5π/2) = undefined, sec(5π/2) = -1, cot(5π/2) = undefined

A) Sketch each angle. B) Find sin θ, cos θ, tan θ, csc θ, sec θ, & cot θ. 28. θ = 4π

sin(4π) = 0, cos(4π) = 1, tan(4π) = 0, csc(4π) = undefined, sec(4π) = 1, cot(4π) = undefined

sin(4π) = 1, cos(4π) = 0, tan(4π) = undefined, csc(4π) = 1, sec(4π) = undefined, cot(4π) = 0

sin(4π) = 0, cos(4π) = -1, tan(4π) = 0, csc(4π) = undefined, sec(4π) = -1, cot(4π) = undefined

sin(4π) = 1, cos(4π) = 1, tan(4π) = 1, csc(4π) = 1, sec(4π) = 1, cot(4π) = 1

A) Sketch each angle. B) Find sin θ, cos θ, tan θ, csc θ, sec θ, & cot θ. 29. θ = -5π/2 What are the correct values for the trigonometric functions at θ = -5π/2?

sin(-5π/2) = -1, cos(-5π/2) = 0, tan(-5π/2) = undefined, csc(-5π/2) = -1, sec(-5π/2) = undefined, cot(-5π/2) = 0

sin(-5π/2) = 0, cos(-5π/2) = 1, tan(-5π/2) = 0, csc(-5π/2) = undefined, sec(-5π/2) = 1, cot(-5π/2) = undefined

sin(-5π/2) = 1, cos(-5π/2) = 0, tan(-5π/2) = undefined, csc(-5π/2) = 1, sec(-5π/2) = undefined, cot(-5π/2) = 0

sin(-5π/2) = 0, cos(-5π/2) = -1, tan(-5π/2) = 0, csc(-5π/2) = undefined, sec(-5π/2) = -1, cot(-5π/2) = undefined

A) Sketch each angle. B) Find sin θ, cos θ, tan θ, csc θ, sec θ, & cot θ. 30. θ = -7π

sin(-7π) = 0, cos(-7π) = -1, tan(-7π) = 0, csc(-7π) = undefined, sec(-7π) = -1, cot(-7π) = undefined

sin(-7π) = 1, cos(-7π) = 0, tan(-7π) = undefined, csc(-7π) = 1, sec(-7π) = undefined, cot(-7π) = 0

sin(-7π) = -1, cos(-7π) = 0, tan(-7π) = undefined, csc(-7π) = -1, sec(-7π) = undefined, cot(-7π) = 0

sin(-7π) = 0, cos(-7π) = 1, tan(-7π) = 0, csc(-7π) = undefined, sec(-7π) = 1, cot(-7π) = undefined

Find the ordered pair on the unit circle for the angle θ = 3π/4.

Ordered pair: (-√2/2, √2/2)

Ordered pair: (-√2/2, -√2/2)

Ordered pair: (√2/2, -√2/2)

07.6 - Radians on the Unit Circle

Authored by Denise Lum

Mathematics

9th - 12th Grade

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07.6 - Radians on the Unit Circle

Convert the angle θ = 135° from degrees to radian measure or radians to degrees, whichever is appropriate. Fill in the blank with the correct answer.

To convert 135° to radians, use the formula: radians = degrees × (π/180). Thus, 135° × (π/180) = 3π/4. Therefore, the correct answer is θ = 3π/4.

Convert the angle θ = 240° from degrees to radian measure or radians to degrees, whichever is appropriate. Fill in the blank with the correct answer.

To convert 240° to radians, use the formula: radians = degrees × (π/180). Thus, 240° × (π/180) = 4π/3. Therefore, the correct answer is θ = 4π/3.

Convert the angle θ = 7π/5 from degrees to radian measure or radians to degrees, whichever is appropriate. Fill in the blank with the correct answer.

To convert radians to degrees, use the formula: degrees = radians × (180/π). For θ = 7π/5, it becomes 7π/5 × (180/π) = 252°. Thus, the correct answer is θ = 252°.

Convert the angle θ = 11π/12 from degrees to radian measure or radians to degrees, whichever is appropriate. Fill in the blank with the correct answer.

To convert radians to degrees, use the formula: degrees = radians × (180/π). For θ = 11π/12, it becomes 11π/12 × (180/π) = 165°. Thus, the correct answer is θ = 165°.

Convert the angle θ = 330° from degrees to radian measure or radians to degrees, whichever is appropriate. Fill in the blank with the correct answer.

To convert 330° to radians, use the formula θ (radians) = θ (degrees) × π/180. Thus, 330° × π/180 = 11π/6. Therefore, the correct answer is θ = 11π/6.

Convert the angle θ = 270° from degrees to radian measure or radians to degrees, whichever is appropriate. Fill in the blank with the correct answer.

To convert 270° to radians, use the formula: radians = degrees × (π/180). Thus, 270° × (π/180) = 3π/2. Therefore, the correct answer is θ = 3π/2.

Convert the angle θ = 15π/8 from degrees to radian measure or radians to degrees, whichever is appropriate. Fill in the blank with the correct answer.

To convert θ = 15π/8 radians to degrees, use the formula: degrees = radians × (180/π). Thus, θ = (15π/8) × (180/π) = 337.5°. Therefore, the correct answer is θ = 337.5°.

Convert the angle θ = 2 from degrees to radian measure or radians to degrees, whichever is appropriate. Fill in the blank with the correct answer.

To convert degrees to radians, use the formula: radians = degrees × (π/180). For θ = 2 degrees, it equals 2 × (π/180) = 0.0349 radians. The correct conversion to degrees is θ = 114.6°, which matches the answer choice.

Convert the angle θ = -3 from degrees to radian measure or radians to degrees, whichever is appropriate. Fill in the blank with the correct answer.

To convert -3 radians to degrees, use the formula: degrees = radians × (180/π). Thus, -3 × (180/π) ≈ -171.9°. Therefore, the correct answer is θ = -171.9°.

Convert the angle θ = -315° from degrees to radian measure or radians to degrees, whichever is appropriate. Fill in the blank with the correct answer.

To convert -315° to radians, add 360° to get 45°. Then, convert 45° to radians: 45° = π/4. Since the original angle is negative, it becomes -7π/4. Thus, θ = -7π/4 is the correct answer.

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