Question

tan theta is undefined for theta = ??

Answer 1

Hint:
\[\Large \tan(\theta) = \frac{\sin(\theta)}{\cos(\theta)}\]

Answer 2

Another hint:
determine what values of theta make \[\Large \cos(\theta) = 0\] true

Answer 3

I dont understand, given my choices are
pi/2
pi
0
3pi/2

Answer 4

do you have the unit circle with you?

Answer 5

no

Answer 6

unit circle

https://upload.wikimedia.org/wikipedia/commons/thumb/4/4c/Unit_circle_angles_color.svg/2000px-Unit_circle_angles_color.svg.png

Answer 7

the x coordinate of each point on the unit circle is equal to the value of `cos(theta)`

do you see any points with x coordinates of 0?

Answer 8

yes
pi/2
3pi/2

Answer 9

yep so those values of theta will make `tan(theta)` undefined

because of the division by zero errors

Answer 10

ie,

cos(pi/2) = 0
cos(3pi/2) = 0

so tan(theta) = sin(theta)/cos(theta) is undefined when theta is pi/2 or 3pi/2

Answer 11

thank you for all your help!

Answer 12

sure thing