Inverse Tan 1 and tan-1(-1)
Examples , Pictures and Significance
The inverse tan of 1 , ie tan-1
(1) is a very special value for the inverse tangent function
. Remember that tan-1
(x) will give you the angle whose tan
is x . Therefore, tan-1
(1) = the angle whose tangent is 1. It's also helpful to think of tangent
The Value of the Inverse Tan of 1
As you can see below, the inverse tan-1 (1)is 45° or, in radian measure, Π/4 . It is helpful to think of tangent as the ratio of sine over cosine, ie : . Therefore, tan(Θ) to equal 1, sin(Θ) and cos(Θ) must have the same value.
So-When do sine and cosine have the exact same value?
The answer is at
and,, of course, sine these trig functions are cyclical you can generalize