sin(x)cos(x)=(√2)/4?

Question

Not sure which identities are used to solve this, going around in circles.

Answer 1

The trigonometric identity to be used is:
sin(2x) = 2 sinxcosx

Solution:
sinxcosx = (sqrt2)/4
multiply both sides by ,
2sinxcosx = (sqrt2)/2
use the identity,
sin(2x) = (sqrt2)/2
the angle whose sine is (sqrt2)/2 is 45 degrees or pi/4,
and 135 degrees or 3pi/4
2x = 45, or 2x = 135
x = 22.5 degrees, or x = 67.5 degrees

Answer 2

Alright let's see.

Oh alright. So if this answer is (√2)/4 you know that you're multiplying 1/2 and √2/2 together because those are values on the unit circle.

SO

wait, if you're trying to solve for x then I'm confused because they can't really be the same variable..

Answer 3

sin(x) cos(x) = √2/4

1/2(2sinx cosx) = √2/4

1/2(sin(2x)) = √2/4

sin(2x) = √2/2 = 1/√2

2x = pi/4, 3pi/4

x = pi/8, 3pi/8

Answer 4

2sinxcosx=sqrt2/2 multiply both sides by 2
sin2x=1/sqrt2
2x=pi/4
x=pi/8
This is one of the solutions.
The second solution is (pi/4+pi)/2
=3pi/8
But if you want to know all the solutions, the answer is pi/8+(2pi)k and 3pi/8+(2pi)k

Answer 5

sin(a+b) = sina*cosb + cosa*sinb
sin(2a) = sina*cosa + cosa*sina

sin2a = 2sina*cosa

sin(a)*cos(a) = sin(2a)/2 = sqrt2/4
sin(2a) = sqrt2/2 = sin45
a = 22.5 (or x in your case, sorry about that)

whoops, janson is right, I forgot to take sin135 into account. 67.5 is also a solution.