Trigonometric Functions on a Circle

Unit Circle and Trig Functions at 90,180, 270 and 360

Find all six trigonometric functions.

Multiple Choice

What is the $$\sin\ \frac{\pi}{2}$$  ?

• $$0$$  

• $$1$$  

• $$Undefined$$  

• $$\pi$$  

Multiple Choice

What is the $$\cos\ \frac{\pi}{2}$$  ?

• $$0$$  

• $$1$$  

• $$-1$$  

• undefined

Multiple Choice

What is the $$\tan\ \frac{\pi}{2}$$  ?

• $$\tan\ \frac{\pi}{2}=0$$  

• $$\tan\ \frac{\pi}{2}=1$$  

• $$\tan\ \frac{\pi}{2}=-1$$  

• $$\tan\ \frac{\pi}{2}=undefined$$  

Multiple Choice

What is the $$\csc\ \frac{\pi}{2}$$  ?

• $$\csc\ \frac{\pi}{2}=0$$  

• $$\csc\ \frac{\pi}{2}=1$$  

• $$\csc\ \frac{\pi}{2}=undefined$$  

Multiple Choice

What is the $$\sec\ \frac{\pi}{2}$$  ?

• $$\sec\ \frac{\pi}{2}=undefined$$  

• $$\sec\ \frac{\pi}{2}=1$$  

• $$\sec\ \frac{\pi}{2}=0$$  

Multiple Choice

$$\cot\ \frac{\pi}{2}=?$$  

• $$\cot\ \frac{\pi}{2}=1$$  

• $$\cot\ \frac{\pi}{2}=0$$  

• $$\cot\ \frac{\pi}{2}=undefined$$  

The stress of the unit circle.

There are many ways people try to remember stuff.

Multiple Select

Which are equal to $$0?$$  

• $$\sin\pi$$  

• $$\cos\pi$$  

• $$\tan\pi$$  

• $$\sec\ \pi$$  

• $$\csc\ \pi$$  

Multiple Select

Which are equal to $$-1?$$  

• $$\sin\pi$$  

• $$\cot\pi$$  

• $$\cos\pi$$  

• $$\sec\pi$$  

Multiple Choice

Which are undefined?

• $$\cos\pi$$

• $$\cot\ \pi$$

• $$\tan\pi$$

Multiple Choice

We know the $$\tan\ \left(\frac{3\pi}{2}\right)$$  is undefined. Which other trig function is undefined at  $$\frac{3\pi}{2}$$  ?

• $$\sec\ \frac{3\pi}{2}$$  

• $$\csc\ \frac{3\pi}{2}$$  

• $$\cot\ \frac{3\pi}{2}$$  

Poll

What is the value of the $$\sin\ 2\pi?$$  (or 360 degrees)

• $$1$$  

• $$0$$  

• $$undefined$$  

Multiple Choice

What is the radius of the unit circle?

• 0
• 1
• 1/2
• √2/2

Poll

How do you feel about the unit circle and the six trigonometric functions?

• I'm getting a better handle on it.

• I still feel unsure about it all.

• It is still overwhelming for me.

• I'd like more practice.