Question

1. Complete the empty cells in the table below with the correct values. sin theta= sqrt 2/2

Answer 1

Using trigonometric function concepts, it is found that:

• The angle is of 45 degrees, or $\frac{\pi}{4}$ radians.

• $\cos{\theta} = \frac{\sqrt{2}}{2}$

• $\csc{\theta} = \sqrt{2}$

• $\sec{\theta} = \sqrt{2}$

• $\cot{\theta} = 1$

From the sine, we have that:

$\sin{\theta} = \frac{\sqrt{2}}{2}$

Then:

$\sin^{-1}{\sin{\theta}} = \sin^{-1}{\frac{\sqrt{2}}{2}}$

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

Since pi radians is 180º, this angle is of 180/4 = 45 degrees.

From the tangent:

$\tan{\theta} = \frac{\sin{\theta}}{\cos{\theta}}$

$1 = \frac{\frac{\sqrt{2}}{2}}{\cos{\theta}}$

$\cos{\theta} = \frac{\sqrt{2}}{2}$

$\cot{\theta} = \frac{1}{\tan{\theta}}$

$\cot{\theta} = 1$

For the cosecant and secant:

$\csc{\theta} = \frac{1}{\sin{\theta}} = \frac{1}{\frac{\sqrt{2}}{2}} = \frac{2}{\sqrt{2}} \times \frac{\sqrt{2}}{\sqrt{2}} = \sqrt{2}$

$\sec{\theta} = \frac{1}{\cos{\theta}} = \frac{1}{\frac{\sqrt{2}}{2}} = \frac{2}{\sqrt{2}} \times \frac{\sqrt{2}}{\sqrt{2}} = \sqrt{2}$

$\csc{\theta} = \sqrt{2}$

$\sec{\theta} = \sqrt{2}$

To learn more about trigonometric functions, you can take a look at https://brainly.com/question/18055768