Using inverse trig functions to find angles

• Nov 3rd 2007, 07:16 PM
overduex
Using inverse trig functions to find angles

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!!!

Attachment 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!
• Nov 3rd 2007, 07:27 PM
Jhevon
Quote:

Originally Posted by overduex

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!!!

Attachment 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:

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

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

now do the second