Practice with Partial Unit Circle

Practice with Partial Reference Circles

6.5 - The Unit Circle

1) a = π/4 2) b = -π/6

• π/4 goes up from the x-axis... (one-quarter slice)

• -π/6 goes down from the x-axis... (one-sixth slice)

Multiple Choice

Which of the following is the x-coordinate associated with π/4?

• $\frac{\sqrt{3}}{2}$

• $-\frac{\sqrt{3}}{2}$

• $\frac{\sqrt{2}}{2}$

• $-\frac{\sqrt{2}}{2}$

• $\frac{1}{2}$

Multiple Choice

Which of the following is the y-coordinate associated with π/4?

• $\frac{\sqrt{3}}{2}$

• $-\frac{\sqrt{3}}{2}$

• $\frac{\sqrt{2}}{2}$

• $-\frac{\sqrt{2}}{2}$

• $\frac{1}{2}$

Multiple Choice

Which of the following is the x-coordinate associated with -π/6?

• $\frac{\sqrt{3}}{2}$

• $-\frac{\sqrt{3}}{2}$

• $\frac{1}{2}$

•  $-\frac{1}{2}$  

Multiple Choice

Which of the following is the y-coordinate associated with -π/6?

• $\frac{\sqrt{3}}{2}$

• $-\frac{\sqrt{3}}{2}$

• $\frac{1}{2}$

•  $-\frac{1}{2}$  

1)  $\alpha=\ \frac{\pi}{4}$  

•  $\sin\left(\frac{\pi}{4}\right)=y\ =\ \frac{\sqrt{2}}{2}$  

•  $\cos\left(\frac{\pi}{4}\right)=x=\frac{\sqrt{2}}{2}$  

•  $\tan\left(\frac{\pi}{4}\right)=\ \frac{y}{x}=\frac{\sqrt{2}\div2}{\sqrt{2}\div2}=1$  

2)  $\beta=\ -\frac{\pi}{6}$  

•  $\sin\left(-\frac{\pi}{6}\right)=y\ =\ -\frac{1}{2}$  

•  $\cos\left(-\frac{\pi}{6}\right)=x=\frac{\sqrt{3}}{2}$  

•  $\tan\left(-\frac{\pi}{6}\right)=\ \frac{y}{x}=\frac{-1\div2}{\sqrt{3}\div2}=-\frac{1}{\sqrt{3}}$  

9.) Cosecant, secant, and cotangent...

• Cosecant is the flip of Sine $\left(\frac{\sqrt{2}}{2}\right)\longleftrightarrow\left(\frac{2}{\sqrt{2}}\right)$  

• Secant is the flip of Cosine

    $\left(-\frac{\sqrt{2}}{2}\right)\longleftrightarrow\left(-\frac{2}{\sqrt{2}}\right)$  

• Cotangent is the flip of Tangent