Question

Without a calculator, determine the exact value of each expression.

sin (π/2)

cos (π/3)

Could someone please explain to me how this problem is solved. I know I did this in Pre-Cal, but I honestly don't remember a thing. Thanks.

Answer 1

do you remember the unit circle?

Answer 2

Sin(pi/2)=Sin(90)
I think sin was the y values
y value at sin 90= 1

Think of the unit circle

Answer 3

here's a unit circle you can use

http://upload.wikimedia.org/wikipedia/commons/thumb/4/4c/Unit_circle_angles_color.svg/1024px-Unit_circle_angles_color.svg.png

Answer 4

what @jim_thompson5910 said
there is a nice unit circle on the last page of the attached cheat sheet
find \(\frac{\pi}{3}\)and look at the corresponding point
the first coordinate is the cosine and the second coordinate is the sine

Answer 5

now what do I do with the unit circle? btw, I need to show all work and + I need the work to understand it myself. There's about 14questions like these two, but I figured if I could understand these two I could do the rest on my own.

Answer 6

do you see on either unit circle given where it has pi/3 as the angle?

Answer 7

i can see why you need to understand this but there is no work to show
it is not a computation like \(7^2\) or something
look at the point on the unit circle corresponding to the angle \(\frac{\pi}{3}\)

Answer 8

you should see the point \((\frac{1}{2},\frac{\sqrt3}{2})\)

Answer 9

the first coordinate is cosine, and the second coordinate is sine
i.e
\[\cos(\frac{\pi}{3})=\frac{1}{2}\\
\sin(\frac{\pi}{3})=\frac{\sqrt3}{2}\]

Answer 10

so there is no actual work to "show" all the work is done with your eyeballs, locating the point you need
then you write the answer

Answer 11

When I took calculus my teacher tested us without providing us with a unit circle. This website might help you memorize it. http://www.mathsisfun.com/geometry/unit-circle.html

Answer 12

Would it be acceptable if for the work I did- Step 1 Find the reference angle, θ' and sin θ'

θ' = 180 - 90 = 90

The function value for the reference angle is sin 90 = 1

Answer 13

that will work, but you can also just state that sin(90) = 1

so sin(pi/2) = 1

as satellite73 is saying, there's not much work to show since you're looking up a table or a diagram (or just stating what you have memorized)

Answer 14

also, here's a great page for reference angles

http://www.mathopenref.com/reference-angle.html

Answer 15

I know there isn't much work, but this is the first assignment for the school year and I just want to make a good impression. Now how would I do tan (7pi/4) tan is equal y/x correct.

Answer 16

yes because tan = sin/cos