# Math Help - Using inverse trig functions to find angles

1. ## Using inverse trig functions to find angles

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!!!

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!

2. 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!!!

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