How do you simplify $sin ({tan}^{- 1} (- 3))$ $sin (tan^-1 (-3))$ ?

Question

How do you simplify $sin ({tan}^{- 1} (- 3))$ $sin (tan^-1 (-3))$ ?

1 Answer

Impact of this question

7644 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2016-07-08T08:04:15

$- \frac{3}{\sqrt{10}}$ $-3/sqrt 10$ , for principal value of ${tan}^{- 1} (- 3)$ $tan^(-1)(-3)$ . The general solution is $\pm \frac{3}{\sqrt{10}}$ $+-3/sqrt 10$ .

Explanation:

Let $a = {tan}^{- 1} (- 3)$ $a=tan^(-1)(-3)$ . Then, $tan a = - 3 < 0$ $tan a = -3<0$ .

So, the principal a is in the fourth quadrant and the general a is in

either fourth or second.

And so, $sin a = - \frac{3}{\sqrt{10}}$ $sin a = -3/sqrt 10$ against principal a and the given

expression

$sin a = - \frac{3}{\sqrt{10}}$ $sin a=-3/sqrt 10$

The general solution is $\pm \frac{3}{\sqrt{10}}$ $+-3/sqrt 10$ .

Science

Math

Humanities

... and beyond

How do you simplify $sin ({tan}^{- 1} (- 3))$ $sin (tan^-1 (-3))$ ?

1 Answer

Explanation:

Related questions

Impact of this question

Science

Math

Humanities

... and beyond

How do you simplify sin(tan−1(−3))sin (tan^-1 (-3))?

1 Answer

Explanation:

Related questions

Impact of this question

How do you simplify $sin ({tan}^{- 1} (- 3))$ $sin (tan^-1 (-3))$ ?