Answered

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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.

Sagot :

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

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

The cosine ratio is given as:

[tex]\cos(\theta) = \frac{\sqrt 3}{2}[/tex]

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

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

[tex]\theta = \frac{\pi}{6}[/tex]    [tex]\theta = \frac{11\pi}{6}[/tex] and [tex]\theta = \frac{13\pi}{6}[/tex]

The value of sec θ

We have:

θ = 495°

Convert to radians

[tex]\theta = 495 * \frac{\pi}{180}[/tex]

Evaluate

[tex]\theta = \frac{11\pi}{4}[/tex]

The value of sec θ is then calculated as:

[tex]\sec(\theta) = \sec(\frac{11\pi}{4})[/tex]

Using a calculator, we have:

[tex]\sec(\theta) = -1.414[/tex]

Hence, the value of [tex]\sec(\theta)[/tex] is -1.414

Read more about trigonometry ratios at:

https://brainly.com/question/27223704

#SPJ1

View image MrRoyal
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