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ZanzabumX [31]
3 years ago
14

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 <span>=x</span>,

adjacent side <span>=1</span>

and 

hypotenuse <span>=<span>√(x</span></span>²+1)

Therefore 

the sine of this angle <span>=<span>opposite side/hypotenuse</span></span>

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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