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3 years ago

Write the composed trigonometric function sin(arctan x) in terms of x

Mathematics

1 answer:

Radda [10]3 years ago

8 0

Let
∅=arc tan x

we know that

∅ is an angle whose tangent function is

tan ∅=x/1

Considering the sides of the right triangle.

We have

opposite side =x,

adjacent side =1

and

hypotenuse =√(x²+1)

Therefore

the sine of this angle =opposite side/hypotenuse

sin ∅=x/√(x²+1)-----> the sign of sine ∅ will depend on the quadrant in which it is located

value of sin ∅ is positive---------> ∅ belong to the first or second quadrant

value of sin ∅ is negative---------> ∅ belong to the third or fourth quadrant

the answer is

x/√(x²+1)

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