Question

if sin theta=11/15 find cos theta and tan theta

Answer 1

Hey mate!!! Here the answer is :-

It is given that :-Sin theta =11/15

Now, we all know that :-Sin theta =Perpendicular /Hypotenuse

Therefore, Perpendicular =11 and Hypotenuse =15

Hence, Using Phythagoras theorem,

(Hypotenuse)^2=(Base)^2+(Perpendicular)^2

=(15)^2=(Base)^2+(11)^2

=225=(Base)^2+121

=225-121=(Base)^2

104=(Base)^2

√104=Base

2√26=Base

Now,

Cos theta=Base/Hypotenuse=2√26/15

Tan theta=Perpendicular/Base=11/2√26

Hope it will help you!!!

Answer 2

Answer:

The value of cosθ =√104/15 and tanθ= 11/√104.

Step-by-step explanation:

Consider that H = hypotenuse, P = perpendicular and B =base

We know

 $Sin\theta=\frac{P}{H} , cos\theta=\frac{B}{H} , Tan\theta=\frac{P}{B}$

It means that P = 11 and H=15

By using Pythagoras theorem;

               $H^{2}=B^{2}+P^{2}\\ B^{2}=H^{2}-P^{2}\\ B=\sqrt{H^{2}-P^{2}} \\ B=\sqrt{(15)^{2}-(11)^{2}}\\ B=\sqrt{104}$

Therefore    $cos\theta=\frac{\sqrt{104} }{15}$     and    $tan\theta=\frac{11}{\sqrt{104} }$