Given that. sin 2x = cos (3x - 10), find tanx
2x = 90 -(3x -10)
2x = 90 -3x + 10
2x = -3x + 100
2x + 3x = -3x + 3x + 100
5x = 100
x = 20
tanx = sin/cos
tan = sin40/cos50
Is that correct
your x = 20 if x is in degrees
so tan x = tan20, which is not a rational number.
my calculator says: .36397...
why are you saying tanx = sin40/cos50 ??
tanx = sinx/cosx = sin20/cos20 = .36397...
Reiny is right to wonder when you wrote:
tan x = sin 40 / cos 50
because
sin( 40° ) = cos( 90° − 40° ) = cos 50°
so
sin 40° / cos 50°= cos 50° / cos 50° = 1
To find the value of tan(x), we first need to find the value of x from the equation sin(2x) = cos(3x - 10).
You correctly solved the equation and found that x = 20.
Now, to find tan(x), we can substitute the value of x into the formula tan(x) = sin(x)/cos(x).
However, it seems like there was a mistake in your final step. The correct values should be sin(40) and cos(50), not sin(40)/cos(50).
So, the correct way to calculate tan(x) using the given value of x = 20 is:
tan(20) = sin(20)/cos(20)
You can use a scientific calculator or reference table to find the numerical values of sin(20) and cos(20) and then divide them to get the value of tan(20).