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Pavlova-9 [17]
2 years ago
6

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

Mathematics
1 answer:
bekas [8.4K]2 years ago
5 0
  • 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

<h3>Three possible angles θ on the domain [0,∞)</h3>

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}

<h3>The value of sec θ</h3>

We have:

θ = 495°

Convert to radians

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

Evaluate

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

<h3 />

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:

brainly.com/question/27223704

#SPJ1

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