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100 POINTS!!!!!!!
Part A: What is a coterminal angle of θ such that 0 ≤ θ ≤ 2π?


Part B: What are the exact values of all six trigonometric functions evaluated at θ?

100 POINTS Part A What Is A Coterminal Angle Of Θ Such That 0 Θ 2π Part B What Are The Exact Values Of All Six Trigonometric Functions Evaluated At Θ class=

Sagot :

sqdancefan

Answer:

  A.  coterminal angle = 4π/3

  B.  sin(θ) = -√3/2; csc(θ) = -2√3/3; cos(θ) = -1/2;

       sec(θ) = -2; tan(θ) = √3; cot(θ) = √3/3

Step-by-step explanation:

A.

Any angle that is a multiple of 2π added to the given angle will be coterminal. You want one in the range [0, 2π], so we need to add 4π to the given angle

  coterminal angle = -8π/3 +4π = -8π/3 +12π/3

  coterminal angle = 4π/3

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B.

The reference angle is 4π/3 -π = π/3. θ is a quadrant III angle, so both the sine and cosine are negative.

  sin(θ) = -√3/2 . . . csc(θ) = -2√3/3

  cos(θ) = -1/2 . . . sec(θ) = -2

  tan(θ) = √3 . . . cot(θ) = √3/3

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