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
