trig question

[msu08]

the value of cos (pi/3) equals the value of

A. -cos 2pi/3
B. cos 2pi/3
C. cos 6pi/3
D. -cos 5pi/3
E. cos 4pi/3

answer is A why????

another ....

for all y, the cos y is equal to which of the following?
A. siny
B. cos(y + pi)
C. sin (-y)
D. sin y+ cos y
E. cos (-y)

answer is E why??
these problems really get me. i know they're not hard, it's just when i look at them, i'm not even sure about what trig info i should be using to solve them. any suggestions about which identities, etc. i should know for the QR section as well as explanations to these problems would be fantastic! thank youu!

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[FutureInternist]

the value of cos (pi/3) equals the value of

A. -cos 2pi/3
B. cos 2pi/3
C. cos 6pi/3
D. -cos 5pi/3
E. cos 4pi/3

answer is A why????

another ....

for all y, the cos y is equal to which of the following?
A. siny
B. cos(y + pi)
C. sin (-y)
D. sin y+ cos y
E. cos (-y)

answer is E why??
these problems really get me. i know they're not hard, it's just when i look at them, i'm not even sure about what trig info i should be using to solve them. any suggestions about which identities, etc. i should know for the QR section as well as explanations to these problems would be fantastic! thank youu!

You have to memorise the unit circle for this, or atleast the first quadrant from which you can derive the rest of the values.

For the first one...cos(pi/3) = 0.5 (i.e. a positive number). Cos of angles are equal when reflected across the x -axis i.e. Cos (pi/3) = Cos (5pi/3)
C is out since that is 2pi & cos 2pi = 1
D is out since cos (pi/3) has the SAME value as cos 5(pi/3) (not it's negative)
E is out since cos (4pi/3) is in the 3rd quad & hence is negative.

That leaves A or B. Again, 2pi/3 is in the 2nd quad & hence its negative so B is out, leaving A as the only option.

For the 2nd Q, again you just have to know it. Taking 60 (pi/3) as an example....
cos 60=0.5
cos 60 = cos -60 = cos300 = 0.5
This also goes back to the first Q in that cos values are the same when reflected across the X-axis.

Hope this helps.
Post any more Qs here.

 

[FutureInternist]

This might help.