Question

Let (3,-2) be a point on the terminal side of theta in standard position. Find exact values of the six trigonometric functions of theta

Answer 1

Answer:

• sin(θ) = (-2√13)/13
• cos(θ) = (3√13)/13
• tan(θ) = -2/3
• sec(θ) = (√13)/3
• csc(θ) = (-√13)/2
• cot(θ) = -3/2

Step-by-step explanation:

The distance of the point from the origin is ...

  r = √(3² +(-2)²) = √13

We know that ...

  x = r·cos(θ)   ⇒   cos(θ) = x/r = 3/√13 = (3√13)/13

  y = r·sin(θ)   ⇒   sin(θ) = y/r = -2/√13 = (-2√13)/13

  tan(θ) = sin(θ)/cos(θ) = -2/3

  sec(θ) = 1/cos(θ) = (√13)/3

  csc(θ) = 1/sin(θ) = (-√13)/2

  cot(θ) = 1/tan(θ) = -3/2