Question

Part 1: Given cosine of theta is equal to radical 3 over 2 comma determine three possible angles θ on the domain [0,∞).

Part 2: Given θ = 495°, convert the value of θ to radians and find sec θ.

Answer 1

• Three values of $\theta$ when $\cos(\theta) = \frac{\sqrt 3}{2}$ are $\theta = \frac{\pi}{6}$    $\theta = \frac{11\pi}{6}$ and $\theta = \frac{13\pi}{6}$
• The value of $\sec(\theta)$ is -1.414

Three possible angles θ on the domain [0,∞)

The cosine ratio is given as:

$\cos(\theta) = \frac{\sqrt 3}{2}$

See attachment for the graph of $\cos(\theta) = \frac{\sqrt 3}{2}$ under the domain of [0,∞)

From the graph, we can see that some values of $\theta$ when $\cos(\theta) = \frac{\sqrt 3}{2}$ are:

$\theta = \frac{\pi}{6}$    $\theta = \frac{11\pi}{6}$ and $\theta = \frac{13\pi}{6}$

The value of sec θ

We have:

θ = 495°

Convert to radians

$\theta = 495 * \frac{\pi}{180}$

Evaluate

$\theta = \frac{11\pi}{4}$

The value of sec θ is then calculated as:

$\sec(\theta) = \sec(\frac{11\pi}{4})$

Using a calculator, we have:

$\sec(\theta) = -1.414$

Hence, the value of $\sec(\theta)$ is -1.414

Read more about trigonometry ratios at:

https://brainly.com/question/27223704

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