Question

Without using a calculator, find the matching value for f in each function. Give exact answers.

Answer 1

\[f=\cos (-\frac{ 3\pi }{ 2 })\]

Answer 2

find the point on the unit circle corresponding to the angle of \(-\frac{3\pi}{2}\)
cosine will be the first coordinate

Answer 3

thats 300 degrees and the first coordinate is 1/2 but thats not the correct answer...:/

Answer 4

oh oh oh i was looking at the coordinates of y

Answer 5

so its 270 degrees.

Answer 6

forget degrees. angles measure in radians
you should be right at the top of the circle at \((0,1)\)

Answer 7

At the top of my circle i have pi/2...

Answer 8

http://www.math.ucsd.edu/~jarmel/math4c/Unit_Circle_Angles.png

Answer 9

yes that is true, but if you go around the circle in the negative direction (clockwise) then you end up at the same point

Answer 10

but how does that change it? you end up at the same place...

Answer 11

hope that is clear
count in units of \(\frac{\pi}{2}\) going the other direction

Answer 12

you do end up in the same place, so the cosine is 0 and the sine is 1

Answer 13

in other words \(\cos(\frac{\pi}{2})=\cos(-\frac{3\pi}{2})\)

Answer 14

both sine and cosine are periodic with period \(2\pi\)

Answer 15

okay, okay i can see that cause if the bottom of the circle is 3pi/2 that the opposite of that would be negative. AKA the upper half of the circle. okay...

Answer 16

or just count, either way

Answer 17

okay it just kinda had to click in my brain.. so f=cos(-3pi/2) is the exact same thing as f=cos(pi/2)