what are the steps to solve this problem? Write each trigonometric expression as an algebraic expression in x 1)sin(tan^-1x) 2)tan(cos^-1x)

At vero eos et accusamus et iusto odio dignissimos ducimus qui blanditiis praesentium voluptatum deleniti atque corrupti quos dolores et quas molestias excepturi sint occaecati cupiditate non provident, similique sunt in culpa qui officia deserunt mollitia animi, id est laborum et dolorum fuga. Et harum quidem rerum facilis est et expedita distinctio. Nam libero tempore, cum soluta nobis est eligendi optio cumque nihil impedit quo minus id quod maxime placeat facere possimus, omnis voluptas assumenda est, omnis dolor repellendus. Itaque earum rerum hic tenetur a sapiente delectus, ut aut reiciendis voluptatibus maiores alias consequatur aut perferendis doloribus asperiores repellat.

Get our expert's

answer on brainly

SEE EXPERT ANSWER

Get your free account and access expert answers to this and thousands of other questions.

A community for students.

what are the steps to solve this problem? Write each trigonometric expression as an algebraic expression in x 1)sin(tan^-1x) 2)tan(cos^-1x)

Mathematics
I got my questions answered at brainly.com in under 10 minutes. Go to brainly.com now for free help!
At vero eos et accusamus et iusto odio dignissimos ducimus qui blanditiis praesentium voluptatum deleniti atque corrupti quos dolores et quas molestias excepturi sint occaecati cupiditate non provident, similique sunt in culpa qui officia deserunt mollitia animi, id est laborum et dolorum fuga. Et harum quidem rerum facilis est et expedita distinctio. Nam libero tempore, cum soluta nobis est eligendi optio cumque nihil impedit quo minus id quod maxime placeat facere possimus, omnis voluptas assumenda est, omnis dolor repellendus. Itaque earum rerum hic tenetur a sapiente delectus, ut aut reiciendis voluptatibus maiores alias consequatur aut perferendis doloribus asperiores repellat.

Get this expert

answer on brainly

SEE EXPERT ANSWER

Get your free account and access expert answers to this and thousands of other questions

Draw a right triangle |dw:1436829693684:dw|
If we let \(\Large \theta = \tan^{-1}(x)\) then \(\Large \tan(\theta) = x = \frac{x}{1}\) because tangent = opposite/adjacent, we can add these labels |dw:1436829773980:dw| making sense so far?
yup :)

Not the answer you are looking for?

Search for more explanations.

Ask your own question

Other answers:

what is the length of the hypotenuse?
r=1^2+x^2 so x^2?
close, but the square root of 1^2+x^2 or the square root of 1+x^2 |dw:1436830005407:dw|
oh okay
with that triangle, you can find sin(theta) remember I made theta be equal to the inverse tangent of x
cos=y/r 1/sqrtx^2+1 1/x+1
hmm I think I did something wrong
you want sine, so sine = opposite/hypotenuse \[\Large \sin(\theta) = \frac{x}{\sqrt{x^2+1}}\] \[\Large \sin\left(\tan^{-1}(x)\right) = \frac{x}{\sqrt{x^2+1}}\]
|dw:1436830701065:dw|
btw, \[\Large \sqrt{x^2+1} \ne x+1\] \[\Large \sqrt{x^2+y^2} \ne x+y\]
and \[\Large \sqrt{A+B} \ne \sqrt{A} + \sqrt{B}\]
oh sorry I didn't know that :o
how would I simplify it?
you can rationalize the denominator, but you can't really do anything else to simplify
I would rationalize it by multiplying both sides by sqrtx^2+1 right?
top and bottom by sqrt(x^2+1)
ohh okay I understand the problem now :)
Rationalizing the denominator gives... \[\Large \sin\left(\tan^{-1}(x)\right) = \frac{x}{\sqrt{x^2+1}}\] \[\Large \sin\left(\tan^{-1}(x)\right) = \frac{x{\color{red}{*\sqrt{x^2+1}}}}{\sqrt{x^2+1}{\color{red}{*\sqrt{x^2+1}}}}\] \[\Large \sin\left(\tan^{-1}(x)\right) = \frac{x\sqrt{x^2+1}}{(\sqrt{x^2+1})^2}\] \[\Large \sin\left(\tan^{-1}(x)\right) = \frac{x\sqrt{x^2+1}}{x^2+1}\] to me, that's not really simplified. If anything, it got more complicated. But some books require you to rationalize the denominator
I see
thank for all your help! I get it now :D sorry it took so much time
that's ok and you're welcome

Not the answer you are looking for?

Search for more explanations.

Ask your own question