Answer:
[tex]cos\Theta =\frac{4}{5}[/tex]
[tex]tan\Theta =\frac{3}{4}[/tex]
Step-by-step explanation:
Given : sin θ = 3/5
To Find : value of cos θ and tan θ
Solution :
use the identity:
[tex]sin^{2}\Theta +cos^{2}\Theta =1[/tex]
putting value of sin θ
⇒ [tex](\frac{3}{5})^{2} + cos^{2}\Theta =1[/tex]
⇒[tex]\frac{9}{25} +cos^{2}\Theta =1[/tex]
⇒[tex]cos^{2}\Theta = 1-\frac{9}{25}[/tex]
⇒[tex]cos^{2}\Theta = \frac{16}{25}[/tex]
⇒[tex]cos\Theta = \sqrt{\frac{16}{25}}[/tex]
⇒[tex]cos\Theta =\frac{4}{5}[/tex]
Thus , [tex]cos\Theta =\frac{4}{5}[/tex]
Now to find value of tan θ
Since we know that
⇒ [tex]tan\Theta =\frac{sin\Theta }{cos\Theta }[/tex] (identity)
⇒[tex]tan\Theta =\frac{\frac{3}{5} }{\frac{4}{5} }[/tex]
⇒[tex]tan\Theta =\frac{3}{5}\div \frac{4}{5}[/tex]
⇒[tex]tan\Theta =\frac{3}{5}\times \frac{5}{4}[/tex]
⇒[tex]tan\Theta =\frac{3}{4}[/tex]
Thus , the value of
[tex]tan\Theta =\frac{3}{4}[/tex]
[tex]cos\Theta =\frac{4}{5}[/tex]
