- 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
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