Question

Angle θ lies in the second quadrant, and sin θ = 3/5. cos θ = tan θ =

Answer 1

The answer is

sin θ = 3/5
we know that 
sin ² θ  + cos² θ  =1, so cos² θ=1 - sin ² θ 
and then  cos θ=sqrt(1 - sin ² θ)

sin θ = 3/5 implies  sin ² θ=(3/5)²=9/25

cos θ=sqrt(1 - 9/25)=cos θ=sqrt(16/25)=4/5

cos θ=4/5

and
tan θ = sin θ/cos θ= (3/5) / (4/5)=3/4

finally 
sin θ = 3/5
cos θ=4/5
tan θ =3/4

Answer 2

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

$tan\Theta =\frac{3}{4}$

$cos\Theta =\frac{4}{5}$