Find out the solution of the equation sinx = cos ?

Expert Answers
hala718 eNotes educator| Certified Educator

sinx= cos x

==> sinx-cosx=0

Square both sides:

==> (sinx-cosx)^2=0

==> sin^2(x) -2sinxcosx +cos^2 x= 0

But sin^2 x + cos^2 x =1

and 2sinx cosx =sin2x

==> 1-sin2x=0

==> sin2x= 1

==> 2x= pi/2

==> x= pi/4

 

neela | Student

To find out the solution of sinx = cos ?

Solution:

If you mean sinx = cos x, then

sinx-cosx = 0. Or

(sinx )(1/sqrt2) -cosx (1/2sqrt) =0. Or

sinx cos (pi/4)- cosx*sin(pi/4) = 0. Or

sin(x-pi/4) = 0. Or

x-pi/4 = npi.

Or

x = npi +pi/4., n=0,1,2....

giorgiana1976 | Student

sin x - cos x = 0

We could divide the equation by (cos x) and the result will be:

sin x /cos x - 1 = 0

tg x -1 = 0

We'll add 1 both sides:

tg x = 1

This is an elementary equation:

x = arctg 1 + k*pi

x = pi/4 + k*pi

pi/4 = 45 degrees.

We could also make the note that if the ratio sin x / cos x = 1, it means that the terms from the ratio are equal

=> sin x = cosx!

If sin x = cos x => the angles  of the triangle are equal too, so, in a right angle triangle, the measures of the angles are of 45 degrees (the conclusion is based on fact that in a triangle, the sum of angles is 180 degrees, and when one of them is 90 degrees, the others, which are equal, are of 45 degrees).

90 + 2*x = 180

2*x =180 - 90

x = 90/2

x = 45 degrees