Evaluate (if possible) the sine, cosine, and tangent at the real number t. (If an answer is undefined, enter UNDEFINED.) t = − π 2 sin t = cos t = tan t =

Question

Evaluate (if possible) the sine, cosine, and tangent at the real number t. (If an answer is undefined, enter UNDEFINED.)

t = − π

2

 

sin t	=
cos t	=
tan t	=

Answer 1

I will assume this is supposed to say -π/2

First recall that this is equivalent to 3π/2. Next recall that (cos(θ),sin(θ))=(x,y)

The coordinates for -π/2 (or 3π/2) on the unit circle is (0,-1).

So sin(t)=sin(-π/2)=-1

Similarly, cos(t)=cos(-π/2)=0

Now recall tan(t)=sin(t)/cos(t)=y/x

So tan(-π/2)=sin(-π/2)/cos(-π/2)=-1/0=undefined because we cannot divide by 0

Hope this helped!