Question

I don’t know how to do this. Can you help please help me ?

Answer 1

Answer:

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

Step-by-step explanation:

See the attached picture for a drawing of the angle and its terminal point coordinates. Those are (cos(4π/3), sin(4π/3)), so we have the following trig function values:

  sin(4π/3) = -√3/2

  cos(4π/3) = -1/2

  tan(4π/3) = sin/cos = √3

  sec(4π/3) = 1/cos = -2

  csc(4π/3) = 1/sin = -(2√3)/3

  cot(4π/3) = 1/tan = (√3)/3

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Additional comment

It helps to know that 1/√a = (√a)/a. This lets you write the ratios with a rational denominator in each case.