Use a right triangle to write the following expression as an algebraic expression. Assume that x is positive and that the given inverse trigonometric function is defined for the expression in x. sin (cos^-1 14x) Show the triangle that is correct to write the given expression as an algebraic expression?

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josealejandrocl josealejandrocl · Answer 1 · 2020-01-03T19:41:30+01:00

Answer:

[tex]Sin(Cos^{-1} (14x))=\sqrt{1-196x^2}[/tex]

Step-by-step explandation:

First of all, from the figure we can define the cosine and sine functions as

[tex]Cos(theta)=\frac{adjacent }{hypotenuse }[/tex]

[tex]Sin(theta)=\frac{Opposite}{hypotenuse }[/tex]

And by analogy with the statement:

[tex]14x=\frac{adjacent }{hypotenuse }[/tex]

Which can be rewritten as:

[tex]\frac{14x}{1}=\frac{adjacent }{hypotenuse }[/tex]

You have then that, for the given triangle, the values of the adjacent and hypotenuse sides, are then given by:

:

Adjacent=14x

Hypotenuse=1

And according to the Pythagorean theorem:

[tex] Opposite=\sqrt{1-(14x)^2}[/tex]

Finally, by doing:

[tex]Cos^-1(14x)=theta[/tex]

We have that:

[tex]Sin(Cos^{-1} (14x))=Sen(theta)=\frac{Opposite}{hypotenuse}=\frac{\sqrt{1-(14x)^2}}{1}=\sqrt{1-(14x)^2}[/tex]