Question

If cos theta 1 + cos theta 2 + cos theta 3 + cos theta 4 + cos theta 5 =5 then sin theta 1 + sin theta 2 + sin then 3 + sin theta 4 + sin theta 5 = ?

Answer 1

Answer:

sin theta1+sin theta2+sin theta3+sin theta4+sin and theta5=5

Step-by-step explanation:

because,if we take theta=0 then cos0=1

so 1+1+1+1+1=5

and cos 0 = sin 90

so,for sin theta..1+1+1+1+1=5

so the answer is 5

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Answer 2

Given: Here we have $\cos {{\theta }_{1}}+\cos {{\theta }_{2}}+\cos {{\theta }_{3}}+\cos {{\theta }_{4}}+\cos {{\theta }_{5}}=5$

To find: we have to find $\sin {{\theta }_{1}}+\sin {{\theta }_{2}}+\sin {{\theta }_{3}}+\sin {{\theta }_{4}}+\sin {{\theta }_{5}}=?$

Solution:

If we take

${{\theta }_{1}}={{\theta }_{2}}={{\theta }_{3}}={{\theta }_{4}}={{\theta }_{5}}=0$

Then we will get the first given equation

$\begin{align} & \cos {{\theta }_{1}}+\cos {{\theta }_{2}}+\cos {{\theta }_{3}}+\cos {{\theta }_{4}}+\cos {{\theta }_{5}}=RHS \\ & \cos 0+\cos 0+\cos 0+\cos 0+\cos 0=RHS \\ & 1+1+1+1+1=RHS \\ & 5=RHS \\ & LHS=RHS \\ \end{align}$

So,

$\begin{align} & \sin {{\theta }_{1}}+\sin {{\theta }_{2}}+\sin {{\theta }_{3}}+\sin {{\theta }_{4}}+\sin {{\theta }_{5}}=? \\ & \sin 0+\sin 0+\sin 0+\sin 0+\sin 0=? \\ & 0+0+0+0+0=? \\ & 0=? \\ \end{align}$

Hence the value of $\sin {{\theta }_{1}}+\sin {{\theta }_{2}}+\sin {{\theta }_{3}}+\sin {{\theta }_{4}}+\sin {{\theta }_{5}}=0$

Final answer:

Hence the answer is 0