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