Question

In given right angled triangle ABC, if angle A = 90°, reference angle B = Theta. Find the trigonometric ratios in the triangle.​

Answer 1

Answer:

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

Step-by-step explanation:

You want the trig functions of θ in the right triangle shown.

SOH CAH TOA

This mnemonic is intended to remind you ...

  Sin = Opposite/Hypotenuse

  Cos = Adjacent/Hypotenuse

  Tan = Opposite/Adjacent

Application

In this triangle, the side opposite angle θ is labeled √3. The side adjacent is labeled 1, and the hypotenuse is labeled 2. This means the trig ratios are ...

  sin(θ) = √3/2

  cos(θ) = 1/2

  tan(θ) = √3/1 = √3

The inverse ratios are ...

  csc(θ) = 1/sin(θ) = 2/√3 = (2√3)/3

  sec(θ) = 1/cos(θ) = 2/1 = 2

  cot(θ) = 1/tan(θ) = 1/√3 = (√3)/3