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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 : tangent ratio. 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
Inverse sine 1 rule

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