Unit Circle Symmetry Reloaded

Suppose  $\cos\theta=x_{\theta}\ \$  and  $\sin\theta=y_{\theta}$  find the values of  $\cos\left(\pi-\theta\right)$  and  $\sin\ \left(\pi-\theta\right)$  

•  $\left(x_{\theta},\ y_{\theta}\right)$  

•  $\left(-x_{\theta},\ y_{\theta}\right)$  

•  $\left(x_{\theta},\ -y_{\theta}\right)$  

•  $\left(-x_{\theta},\ -y_{\theta}\right)$  

Suppose  $\cos\theta=x_{\theta}\ \$  and  $\sin\theta=y_{\theta}$  find the values of  $\cos\left(\pi+\theta\right)$  and  $\sin\ \left(\pi+\theta\right)$  

•  $\left(x_{\theta},\ y_{\theta}\right)$  

•  $\left(-x_{\theta},\ y_{\theta}\right)$  

•  $\left(x_{\theta},\ -y_{\theta}\right)$  

•  $\left(-x_{\theta},\ -y_{\theta}\right)$  

Suppose  $\cos\theta=x_{\theta}\ \$  and  $\sin\theta=y_{\theta}$  find the values of  $\cos\left(-\theta\right)$  and  $\sin\ \left(-\theta\right)$  

•  $\left(x_{\theta},\ y_{\theta}\right)$  

•  $\left(-x_{\theta},\ y_{\theta}\right)$  

•  $\left(x_{\theta},\ -y_{\theta}\right)$  

•  $\left(-x_{\theta},\ -y_{\theta}\right)$  

Which rotation results in flipping the point on the unit circle over the x axis.

• $\pi-\theta$

• $\theta+\pi$

• $-\theta\ or\ 2\pi-\theta$

• $\theta+2\pi$

Which rotation results in flipping the point on the unit circle over the y axis.

• $\pi-\theta$

• $\theta+\pi$

•  $-\theta\ or\ \ 2\pi-\theta$ 

• $\theta+2\pi$

Which rotation results in flipping the point on the unit circle over the origin

• $\pi-\theta$

• $\theta+\pi$

•  $-\theta\ or\ \ 2\pi-\theta$ 

• $\theta+2\pi$

 $\cos\theta=0.87\$  and  $\sin\theta=0.50$  find the values of  $\cos\left(\pi-\theta\right)$  and  $\sin\left(\pi-\theta\right)$  

•  $\left(0.87,0.50\right)$  

•  $\left(-0.87,\ 0.50\right)$  

•  $\left(0.87,\ -0.50\right)$  

•  $\left(-0.87,-0.50\right)$  

Based on the diagram select all the statements that are true

• The coordinates of P' are (x,-y)

• The coordinates of P' are (-x, y)

• The value of $\sin\left(-\theta\right)\$ is equal to the value of $\sin\ \left(\theta\right)$

• The value of $\sin\ \left(-\theta\right)$ is equal to the opposite value of $\sin\left(\theta\right)$

Based on the diagram select all the statements that are true 

• The coordinates of P' are (x,-y)

• The coordinates of P' are (-x, y)

• The value of $\cos\left(-\theta\right)\$ is equal to the value of $\cos\ \left(\theta\right)$

• The value of $\cos\ \left(-\theta\right)$ is equal to the opposite value of $\cos\left(\theta\right)$

Based on the diagram select the statement  that is true

• The coordinates of P' are  $\left(\cos\theta,-\sin\theta\right)$  

• The coordinates of P' are  $\left(-\cos\theta,-\sin\theta\right)$  

• The coordinate of P' are  $\left(-\cos\theta,\ \sin\theta\right)$