Question

Find the values of the trigonometric functions of θ from the information given.

Answer 1

Answer:

• sin(θ) = -(4√15)/17
• cos(θ) = 7/17 . . . . . . . given
• tan(θ) = -(4√15)/7
• csc(θ) = -(17√15)/60
• sec(θ) = 17/7
• cot(θ) = -(7√15)/60

Step-by-step explanation:

The relationship between sine and cosine is ...

  sin² + cos² = 1

Solving for sine gives ...

  sin = ±√(1 -cos²)

In this problem, we want the negative root.

  sin(θ) = -√(1 -(7/17)²) = -√(240/289) = -(4√15)/17

  tan(θ) = sin(θ)/cos(θ) = ((-4√15)/17)/(7/17) = -(4√15)/7

___

And the inverse functions are ...

  sec(θ) = 1/cos(θ) = 17/7

  csc(θ) = 1/sin(θ) = -17/(4√15) = -(17√15)/60

  cot(θ) = 1/tan(θ) = -(7√15)/60

_____

Of course, you're aware that 1/√15 = (√15)/15.