Question

Select all the correct answers.3xIf the measure of angle 8 is , which statements are true?The measure of the reference angle is 45°The measure of the reference angle is 60°.sin() = 2V2o cos(0) = 12tan(0) = 1The measure of the reference angle is 30°-

Answer 1

Answer with Explanation: The provided angle theta is:

`\theta=(3)/(4)\pi r=135^(\circ)`

According to the unit circle, we have the following:

Therefore the (1) sin(theta) , (2) cos(theta) and (3) tan(theta) are as follows:

(1)

`\begin{gathered} sin(\theta)=\frac{\text{ Opposite}}{\text{ Hypotenuse}} \\ sin(\theta)=(√(2))/(2)/1=(√(2))/(2) \\ sin(\theta)=(√(2))/(2) \end{gathered}`

(2)

`\begin{gathered} cos(\theta)=\frac{\text{ Adjacent}}{\text{ Hypotenuse}}=-(√(2))/(2)/1=-(√(2))/(2) \\ cos(\theta)=-(√(2))/(2) \end{gathered}`

(3)

`\begin{gathered} tan(\theta)=\frac{\text{ Opposite}}{\text{ Adjacent}}=(√(2))/(2)/-(√(2))/(2)=-1 \\ tan(\theta)=-1 \end{gathered}`

The measure of the refrence angle is:

`\theta_r=180^(\circ)-135^(\circ)=45^(\circ)`

In conclusion, therefore the only true statements are as follows: