# If 5*sin x = 5*cos x, what is x?

justaguide | College Teacher | (Level 2) Distinguished Educator

Posted on

We have to find x given that 5*sin x = 5*cos x

5*sin x = 5*cos x

=> sin x = cos x

=> sin x / cos x = 1

=> tan x = 1

=> x = arc tan (1)

=> x = 45 degrees

As the tan function is periodic with a periodicity of 180 degrees, x = 45 + n*180 degrees

The value of x is 45 + n*180 degrees.

shaznl1 | High School Teacher | (Level 1) Salutatorian

Posted on

let theta = x

The whole equation becomes

5 sin x = 5 cos x

divide both sides by 5

we get

sin x = cos x

then since sin x =  cos (pi/2 - x)

then the equation becomes

cos (pi/2-x) = cos x

pi/2 - x = x

x= pi/4

of course, since cos and sin are like waves, this equation have multiple answers

sin and cos rotate in a cycle of  2pi

and sin and cos grphs meet two times per cycle

the general theta answer = pi/4 + kpi

k is a whole number constant

for degree answers, it is 45 + k180

k is a whole number constant

hope this helps