Question

Find θ for 0 degrees < θ < 360 degrees cos θ= 0.7361

Answer 1

Given the equation:

`\begin{gathered} \cos\theta=0.7361 \\ for\text{ 0}\leq\theta<360 \end{gathered}`

To find the values of θ, we take the inverse cosine of both sides,

Thus,

`\begin{gathered} cos^(-1)(cos\theta)=cos^(-1)(0.7361) \\ \implies\theta=42.59975343 \end{gathered}`

The cosine of θ is also positive at the 4th quadrant.

Thus, at the 4th quadrant, the value of θ is

`\begin{gathered} \theta^(\prime)=360-\theta \\ \implies\theta^(\prime)=360-42.59975343 \\ =317.4002466 \end{gathered}`

Hence, the values of θ, to 2 decimal places, for 0 °≤ θ < 360° are

`\theta=42.60,\text{ 317.40 }`