Question

Evaluate the expression without using a calculator.

Answer 1

\[\sin (\pi/3) + \cos (\pi/3)\]

Answer 2

An entry level explanation would be useful.

Answer 3

Pi/3=60º
as is well known cos60º=1/2 and sin60º=sqrt3/2

Answer 4

Should I have converted them to degrees then?

Answer 5

allow me to disagree with @myko
this question has nothing to do with degrees.
forget degrees
it has to do with numbers
find the sine and cosine from the coordinates on the unit circle

Answer 6

if it is more clear for you, then yes, if not just stay with radians

Answer 7

do not start a trig problem by converting numbers to degrees, it is a bad habit and will mess you up later
if you are working with numbers, stick with numbers

Answer 8

degrees are just, sometimes, more evident to place a apoint in the circle. But I agree with @satellite73 that it is more strait with rad

Answer 9

sine and cosine are functions of numbers, not angles. they correspond to the functions of angles if the angles are measured in radians

Answer 10

alright that seems to make sense. Will you walk me through what you mean by "find the sine and cosine from the coordinates on the unit circle?"

Answer 11

look at the last page of the cheat sheet i sent
locate the point on the unit circle corresponding to \(\frac{\pi}{3}\) 2x ^{5}+x ^{3}-7x+14

Answer 12

corresponding to \(\frac{\pi}{3}\)

Answer 13

alright I see an ordered pair that looks suspiciously like sin and cos that you mentioned earlier

Answer 14

you should see the ordered pair \((\frac{1}{2},\frac{\sqrt{3}}{2})\)
the first coordinate is \(\cos(\frac{\pi}{3})\) and the second coordinate is \(\sin(\frac{\pi}{3})\)

Answer 15

So what if this is on a test and I'm not allowed the cheat sheet?

Answer 16

This one seems fairly easy now I know this forms a 60 30 90 triangle but what about something more irregular or do these always form 30-60-90 or 45-45-90 triangles?

Answer 17

@satellite73

Answer 18

(The ones they ask me to solve without a calculator.)

Answer 19

@satellite73