If $cos \theta_{1} +cos \theta_{2}+cos \theta_{3}+cos \theta_{4}+cos \theta_{5} = 5$, find the value of $sin \theta_{1} +sin \theta_{2}+sin \theta_{3}+sin \theta_{4}+sin \theta_{5}$.

Given :

$cos \theta_{1} +cos \theta_{2}+cos \theta_{3}+cos \theta_{4}+cos \theta_{5} = 5$.

To do :

We have to find the value of $sin \theta_{1} +sin \theta_{2}+sin \theta_{3}+sin \theta_{4}+sin \theta_{5}$.

Solution :

$cos \theta_{1} +cos \theta_{2}+cos \theta_{3}+cos \theta_{4}+cos \theta_{5} = 5$

We know that,

cos 0° $=$ 1

$ \theta_{1}= \theta_{2}= \theta_{3}= \theta_{4}= \theta_{5}=1$

$1+1+1+1+1 = 5$

So, $\theta = 0°$.

sin 0° $=$ 0

$sin \theta_{1} +sin \theta_{2}+sin \theta_{3}+sin \theta_{4}+sin \theta_{5}= 0+0+0+0+0 = 0$.

Therefore, the value of $sin \theta_{1} +sin \theta_{2}+sin \theta_{3}+sin \theta_{4}+sin \theta_{5}$ is 0.

$cos\theta _{1} +cos\theta _{2} +cos\theta _{3} +cos\theta _{4} +cos\theta _{5} =5$