Find Sin (arcsin 1/6) and Tan(sin^-1 2/7)

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jeew-m | College Teacher | (Level 1) Educator Emeritus

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Assume we have an angle `theta` .

If we need to find the sine value of it we have to calculate `sintheta` .

Suppose we have the value of `sintheta` . We need to find the value of `theta` . Then what should we do. Then we have to find `arcsintheta` . Or in other words `sin^(-1)theta` .

If `sintheta = k` then `arcsink = theta`
This is similar for other trigonometric notations too.

`sin (arcsin 1/6)`

If `sintheta = k` then `arcsink = theta`

`arcsink = theta`

Let `k = 1/6`

`arcsin(1/6) = theta`

`sin(arcsin 1/6) = sintheta`

But we know that s`intheta = k`

`sintheta = 1/6`

`sin(arcsin(1/6)) = 1/6`

So the answer is `sin(arcsin(1/6)) = 1/6` .

`tan(sin^-1 2/7)`

`2/7 = 0.286`

`sin^(0.286) = 16.6deg`

`sin^(-1)(2/7) = 16.6deg`

`tan(sin^-1 (2/7)) = tan16.6 = 0.298`

So the answer is;

`tan(sin^-1 (2/7)) = 0.298`

Sources:

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