Question

Which of the following choices is the value of cscθ given that cosθ= √2/2?

Answer 1

For the cosecant we will get:

   $csc(\pm \frac{pi}{4}) = \frac{1}{sin(\pm \frac{pi}{4})} = \pm \frac{2}{\sqrt{2} } = \pm \sqrt{2}$

So the correct option is the third one.

Which of the following choices is the value of cscθ given that cosθ= √2/2?

First, we can write:

$csc(x) = \frac{1}{sin(x)}$

Now, remember that:

$cos(x) = \frac{\sqrt{2} }{2} \\\\for\ x = \pm \frac{pi}{4}$

And for the sine we have:

$sin(pi/4) = \frac{\sqrt{2} }{2} \\\\sin(-pi/4) = -\frac{\sqrt{2} }{2}$

Then the cosecant for these possible values of x gives:

$csc(\pm \frac{pi}{4}) = \frac{1}{sin(\pm \frac{pi}{4})} = \pm \frac{2}{\sqrt{2} } = \pm \sqrt{2}$

So the correct option is the third one.

If you want to learn more about trigonometric functions:

brainly.com/question/7331447

#SPJ1