Adding sin plus cos with fractions containing square roots

[teffany]

How do I solve:

[sin (pi/3)] + [cos (pi/6)]? <--- "pi" is 3.14...

I think that [sin (pi/3)]= (square root 3) divided by 2

AND that [cos (pi/6)]= (square root 3) divided by 2.

Now I can't remember how to add fractions containing square roots.

My textbook says the answer is: square root 3.

I just have NO IDEA how to get there.

Please help! Thanks in advance.

 

[teffany]

Sorry... I just read that this forum isn't for getting homework help. But I don't know how to move this post, so if somebody in here could help me, I'd appreciate it.

 

[berkeman]

No worries. You may have noticed that it took only nanoseconds for your post to get moved to Homework Help :-)

Are you allowed to use a calculator, or do you need to use tables, or are you supposed to use some other methods?

 

[teffany]

Wow... A+ for getting my post the heck out of dodge.

Calculators are permitted; but I can't get mine to cooperate. There is a "Trigonometric Functions of Special Angles" table in our textbook and I see that the sin pi/3 = (square root 3)/2, and that cos pi/6 = (square root 3)/2.

Sine my original post, I converted radians to degrees to see if that would work, and it did... kind of.

For the sin part of the problem, the radians = 60 degrees. The sin of 60 degrees is .8660.

For the cos part of the problem, the radians = 30 degrees. The cos of 30 degrees is .8660.

I realize .8660 + .8660 = 1.732 which is THE SQUARE ROOT OF 3.

But, how am I supposed to know 1.732 = the square root of 3 on my own? (The book says the answer is the square root of 3.)

I'm assuming I went about the problem differently, so I would now like to know how to work it using square roots.

 

[HallsofIvy]

You are going to (or should!) feel very silly about this. You add fractions with square roots the same way you add any fractions: by getting a common denominator. Since you already have a common denominator, 2, you just add the numerators. Or, since the fractions happen to be identical here, use "a+ a= 2a"! What is 2 times sqrt(3)/2?

 

[teffany]

Could the equation look like this?

sqrt(3)/2 + sqrt(3)/2 = sqrt(6)/2 = sqrt(3)/1 = sqrt(3)

 

[Borek]

$$\frac {\sqrt 3} 2 + \frac { \sqrt 3} 2 = \frac { 2 \sqrt 3} 2 = \sqrt 3$$

It doesn't get any simpler

Note: what you did was awfully wrong You can't add square roots this way. Think about it: if sqrt(4) + sqrt(4) = sqrt(8) then 2+2=sqrt(8), or 4²=8. Obviously that's wrong.

 

[teffany]

Oh! I finally get it! Thank you SO MUCH! I have seen the light of adding square roots.

 

[HallsofIvy]

Yes, it is exactly like adding anything else: x/2+ x/2= 2x/2= x no matter what x is.