Question

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?

Answer 1

`Sin(Cos^(-1) (14x))=√(1-196x^2)`

Step-by-step explandation:

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

`Cos(theta)=(adjacent )/(hypotenuse )`

`Sin(theta)=(Opposite)/(hypotenuse )`

And by analogy with the statement:

`14x=(adjacent )/(hypotenuse )`

Which can be rewritten as:

`(14x)/(1)=(adjacent )/(hypotenuse )`

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:

`Opposite=√(1-(14x)^2)`

Finally, by doing:

`Cos^-1(14x)=theta`

We have that:

`Sin(Cos^(-1) (14x))=Sen(theta)=(Opposite)/(hypotenuse)=(√(1-(14x)^2))/(1)=√(1-(14x)^2)`