help me with my homework lolz.

(Sin 60 + cos 60)2

show your work.

Learn your basic trig/get a calculator.

= (sqrt(3)/2 + 1/2)2
= sqrt(3) + 1

Ouch my bad, this is the problem

(Sin 60 + cos 60)^2

I'm not a math guy, but could you rewrite it as:


Sin 60 ^2 + cos 60^2= 1

That's an identity right?

>>4

The back of the book has (2+sqrt(3))/2, but I have no idea how to get there.

>>4
That's an identity, but it's not equal to >>3

(Sin 60 + cos 60)² =
(Sin 60)² + (cos 60)² + 2 sin 60 cos 60 =
1 + 2 sin 60 cos 60 =
1 + sin 60 =
1 + sqrt(3)/2

>>6 Thanks

>>7
lol

>>4

Why are you on this board?

>>6
Second to last line should be 1 + sin(120).

>>10
no it shouldn't.  the sin^2+cos^2 give us our 1, and the 2*sin(60)*cos(60) becomes 2*sin(60)*.5 = sin(60)  Thus the second to last line is 1+sin(60)

>>11
Or, you know, you could use 2*sin(x)*cos(x) = sin(2*x). But hey, guess I shouldn't expect anyone here to have a high school education.

>>12
So why are you trying to make it more complicated?  Because of how common these angles are, you should know off the top of your head the sine and cosine of 0, 30, 45, 60, and 90.  Hell, you could have it as 1+cos(2*x-90) or 1+cos(2*x)/(tan(2*x)^-1).  Using that identity can be really useful if you don't know x; especially when you are taking a directive or integral. But when you know the angle, especially when it is one of the 5 common angles there is no reason to make it more complicated.

SPOILER: sin 60 = sin 120

You are making a hidden assumption that we are using degrees, though. Though the number '60' kind of indicates that, it was never explicitly stated. Thus, the correct response to this question is arrogance and pedantery.

>>13
Why the fuck simplify it at all then? sin(60) = sqrt(3)/2, cos(60) = 1/2, sin(60) + cos(60) = (1+sqrt(3))/2, ((1+sqrt(3))/2)^2 = (1 + 2sqrt(3) + 3)/4 = 1 + sqrt(3)/2. If you're going to evaluate both sin(60) and cos(60) then just do the fucking problem the way it was given.