Question

In Problems 45–56, use a calculator to solve each equation on the interval . Round answers to two decimal places.
$\cos \theta =-0.9$

Short answer

The solution of the given equation is$\left\{2.69,3.59\right\}$

Step-by-step solution

Step 1. Given Information 

In the given problems we have to use a calculator to solve each equation on the interval and round answers to two decimal places.
$\cos \theta =-0.9$

Step 2. To solve cosθ=-0.9 on a calculator, first set the mode to radians.

Then use the ${\cos }^{-1}$key to obtain

$$\begin{gathered} \theta ={\cos }^{-1}\left(-0.9\right) \\ \theta \approx 2.69056 \end{gathered}$$

Rounded to two decimal places, $\theta =2.69$radian.

Step 3. Since cosine function is positive in fourth quadrant so we can use the identify cos2π-θ=cosθ

To find the second solution within $[0,2\mathrm{\pi })$

$$\begin{gathered} \mathrm{\theta }=2\mathrm{\pi }-2.69 \\ \mathrm{\theta }=3.59 \end{gathered}$$

So the solution set is$\left\{2.69,3.59\right\}$.