Question

explain cosx=1/sqrt2 = pi/4

Answer 1

Hi there

Answer 2

Do you need help?

Answer 3

yes

Answer 4

OKay, do you know what 1/sqrt2 is if you rationalize the denominator?

Answer 5

Multiply sqrt 2 by top and bottom

Answer 6

ok sqrt2/2

Answer 7

Right, Now do you know what the unit circle is?

Answer 8

yes, i see it equals pi/4 now, so i just had to rationalize the denominator

Answer 9

Yes.

Answer 10

Does this explain why it is so?

Answer 11

then how is sin (pi/4) = 1/sqrt2?

Answer 12

Sin is the y value on the unit circle, and cos is the x value

Answer 13

yes

Answer 14

so, you stated earlier, 1/sqrt 2 is the same as sqrt2/2. This applies to this question also.

Answer 15

if you find sin(pi/4) on the unit circle what does it equal?

Answer 16

sqrt2/2

Answer 17

and sqrt2/2 is the same as 1/sqrt2

Answer 18

but what about the sin?

Answer 19

What do you mean about sin?

Answer 20

sin pi/4 = 1/sqrt2, is there a way to compute from here to find the answer is 1/sqrt2

Answer 21

multiply top and bottom by sqrt 2

Answer 22

It works both ways, So say you have 1/sqrt2, and you want the value that shows on the unit circle, multiply top and bottom by sqrt2. You'll get sqrt2/2.

Answer 23

oh, i see. thank you, i understand now!

Answer 24

cool