Question

I need help solving this problem:

solve for x. round to the nearest tenth.

Tan(x°) = 10/8

this isn't for a test just the study guide.

Answer 1

in short

$\bf tan^{-1}[tan(\theta )]=\theta \qquad \qquad sin^{-1}[sin(\theta )]=\theta\qquad \quad cos^{-1}[cos(\theta )]=\theta\\\\ -------------------------------\\\\ %Tan(x°) = 10/8 tan(x^o)=\cfrac{10}{8}\implies tan^{-1}[tan(x^o)]=tan^{-1}\left( \cfrac{10}{8} \right) \\\\\\ \measuredangle x=tan^{-1}\left( \cfrac{10}{8} \right)$

make sure your calculator is in Degrees mode.

Answer 2

The easy way is just to use your calculator;
*The calculator I give example at is CASIO fx-#ES
press shift at the upper left corner, then press tan.
This will give you tan^-1, which is called tan inverse, which is the inverse of the given function tanx.
So, tan^-1(10/8)=x which approximately is, 51.3°