Question

question 7 (1 point)
determine the value of θ to the nearest degree if cotθ = 0.75.
a) 45°
b) 37°
c) 53°
d) 42°

Explanation:

Step1: Recall the relationship between cotangent and tangent

Since \(\cot\theta=\frac{1}{\tan\theta}\), if \(\cot\theta = 0.75\), then \(\tan\theta=\frac{1}{0.75}=\frac{4}{3}\approx1.333\).

Step2: Use the inverse - tangent function

We know that \(\theta=\tan^{- 1}(x)\), where \(x = \frac{4}{3}\). Using a calculator, \(\theta=\tan^{-1}(\frac{4}{3})\).
When we calculate \(\tan^{-1}(1.333)\) on a calculator (in degree mode), \(\theta\approx53^{\circ}\).

Answer:

C. \(53^{\circ}\)