Question

If $sin\theta =\frac{4}{5}$, find the value of $cos\theta$ and $tan\theta$ .

• A. $\frac{3}{5},\frac{3}{4}$
• B. $\frac{4}{5},\frac{3}{4}$
• C. $\frac{3}{5},\frac{4}{3}$
• D. $\frac{4}{5},\frac{4}{3}$

Answer 1

The correct option is C $\frac{3}{5},\frac{4}{3}$

$sin\theta =\frac{4}{5}$
$Perpendicular=4k$,$Hypotenuse=5k$
Using Pythagoras theorem
$Bas{e}^2+Perpendicula{r}^2=Hypotenus{e}^2$
$Base=\sqrt{Hypotenus{e}^2-Perpendicula{r}^2}$
$Base=\sqrt{(5k{)}^2-(4k{)}^2}=3k$

$cos\theta =\frac{Base}{Hypotenuse}=\frac{3k}{5k}=\frac{3}{5}$

$tan\theta =\frac{Perpendicular}{Base}=\frac{4k}{3k}=\frac{4}{3}$