find a solution to 3cos(θ)=−0.862 in radians

$3cos(\theta) = -0.862$
$\frac{3cos(\theta)}{3} = \frac{-0.862}{3}$
$cos(\theta) = -\frac{431}{1500}$
$cos^{-1}[cos(\theta)] = cos^{-1}(-\frac{431}{1500})$
$\theta = 106.6983737\°$
$\theta = 1.86223792^{r}$

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MrRoyal MrRoyal · Answer 2 · 2021-11-18T04:17:56-05:00

The measure of angles can be expressed in degrees or radians

The solution of $\mathbf{3cos(\theta) = -0.862}$ is $\mathbf{\theta = 1.86\ rad}$

The equation is given as:

$\mathbf{3cos(\theta) = -0.862}$

Divide both sides of the equation by 3

$\mathbf{cos(\theta) = -0.2873}$

Take arccos of both sides

$\mathbf{cos^{-1}(cos(\theta)) = cos^{-1}(-0.2873)}$

Simplify the left-hand side

$\mathbf{\theta = cos^{-1}(-0.2873)}$

Using a calculator, take the arccos of the right-hand side, in radians

$\mathbf{\theta = 1.86\ rad}$

Hence, the solution of $\mathbf{3cos(\theta) = -0.862}$ is $\mathbf{\theta = 1.86\ rad}$