Find the values of x , valid between -pi and pi . I am confused because of the range .
sin x =cos x
My attempt .
tan x =1
so x will be 45 .. yes this is when x is between 0 and pi but how bout -pi and 0 ?? thanks
sin x = cos x,
sin x/cos x = 1,
tan x = 1,
x = pi/4 + pi (k), where k is an integer, for domain -pi to pi,
let k = -1 and 0
(1) k = 0,
x = pi/4,
(2) k = -1,
x = pi/4 - pi = -(3/4)pi
see graph, ist quadrant sin x and cos x are positive, in the 3rd quadrant, both are negative.
If you need a different way to show why
tan(x) = 1, draw the triangle with angle x with the opposite and adjacent sides equal to 1 [in the first quadrant]
The hypotenuse is then sqrt(2), and you should recognize that the triangle is a special traingle most likely focused on in your class, where the angle of x is pi/4 radians (the reference angle)