Question

Let tan0= 3/4 and 0 be in Q3
Choose all answers that are correct

Answer 1

Correct choices

`\csc (\theta) = - (5)/(3) \quad \quad \text{2nd option}\\\\\cot(\theta) = (4)/(3) \quad \quad \text{3rd option}\\\\\cos(\theta) = -(4)/(5) \quad \quad \text{4th option}\\\\`

Explanation:

`\text{If \;$ \tan\theta = (3)/(4) $}} \\\\\text{then }\\\theta = \tan^(-1) \left((3)/(4)\right)\\\\= 36.87^\circ \text{ in Q1}\\`

But since tan θ is periodic it will also be 3/4 in Q3 which is 180° + 36.87 = 216.87°

• sin θ is negative in Q3 with sin(216.87) = - 3/5
  so this choice is incorrect
  
• csc (θ) = 1/(sin θ) = -5/3 so correct
  
• cot (θ) = 1/tan (θ) = 4/3 so correct
  
• cos(θ) =cos(216.87) = -4/5 so correct
  
• sec(θ) = 1/cos(θ) = -5/4 so this choice is incorrect