Question

If sin theta =3/5 and theta is an acute angle find ; cos theta and tan theta

Answer 1

$cos \theta = \frac{4}{5} \: \: \: and \: \: \: tan \theta = \frac{3}{4}$

Step-by-step explanation:

$Given, \: \: sin \theta = \frac{3}{5} \\ we \: \: know \: \: \boxed{cos^{2} \theta = 1 - sin^{2} \theta } \\ Now, \: \: \: putting \: \: value \\ cos^{2} \theta = 1 - ( \frac{3}{5} )^{2} \\ cos^{2} \theta = 1 - \frac{9}{25} \\ cos^{2} \theta = \frac{25 - 9}{25} \\ cos^{2} \theta = \frac{16}{25} \\ cos \theta = \sqrt{ \frac{16}{25} } \\ \boxed{ cos \theta = \frac{4}{5} } \\ Now, \: \: \: tan \theta = \frac{sin \theta}{cos \theta} \\ putting \: \: values \\ tan \theta = \frac{ \frac{3}{5} }{ \frac{4}{5} } \\ tan \theta = \frac{3}{5} \times \frac{5}{4} \\ \boxed{tan \theta = \frac{3}{4} }$

Answer 2

Concept: This is the question of Trigonometry.  Trigonometry is based on a Right-angled triangle. In a right-angled triangle Hypotenuse is the largest side and it is given by

$hypotenuse^{2}= perpendicular^{2}+base^{2}$

and other related terms are

$sin$Ф$=$ $\frac{Perpendicular}{hypotenuse}$ , $cos$Ф$=\frac{base}{hypotenuse}$, $tan$Ф$= \frac{perpendicular}{base}$

Given:

$sin$Ф= $\frac{3}{5}$ ,  perpendicular= 3, hypotenuse=5

To find:

CosФ and tanФ

Solution:

base = $\sqrt{hypotenuse^{2}-perpendicular^{2} }$
        = $\sqrt{5^{2}-3^{2} }$

        $= \sqrt{25-9} \\\\= \sqrt{16\\\\= 4$

CosФ = $\frac{4}{5}$  ,  tanФ= $\frac{3}{4}$