Using inverse trig functions to find angles

**overduex** · November 3rd 2007, 07:16 PM

Hi, can anyone please help? I 'm not sure what I'm supposed to do...

the directions are: Use an inverse trigonometric function to write theta as a function of x.

Below I've drawn out 2 of the problems... if you could do just one,I would really appreciate it so I could finish the others.... thank you!!!

$Using inverse trig functions to find angles-math-problems.jpg$

just in case the drawing is not clear,
the first problems reads x+2 is opposite of theta, 5 is the hypotenuse.
the second problem reads x is opposite of theta, 4 is adjacent.

thanks again!

**Jhevon** · November 3rd 2007, 07:27 PM

Originally Posted by overduex

Hi, can anyone please help? I 'm not sure what I'm supposed to do...

the directions are: Use an inverse trigonometric function to write theta as a function of x.

Below I've drawn out 2 of the problems... if you could do just one,I would really appreciate it so I could finish the others.... thank you!!!

$Click image for larger version. Name: math problems.jpg Views: 112 Size: 46.8 KB ID: 4371$

just in case the drawing is not clear,
the first problems reads x+2 is opposite of theta, 5 is the hypotenuse.
the second problem reads x is opposite of theta, 4 is adjacent.

thanks again!

i'll do the first, the second is similar

By the sine trig ratio:

$\sin \theta = \frac {\mbox{Opposite}}{\mbox{Hypotenuse}} = \frac {x + 2}{5}$

$\Rightarrow \theta = \sin^{-1} \left( \frac {x + 2}5 \right)$

now do the second

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