Question

Find exact value of given expression Sin(2 cos^-1(7/25))

Answer 1

`\sin\left(2\cos^(-1)\frac7{25}\right)=2\sin\left(\cos^(-1)\frac7{25}\right)\cos\left(\cos^(-1)\frac7{25}\right)`

`=2(24)/(25)\frac7{25}`

`=(336)/(625)`

Answer 2

0.5377

Explanation:

the correct expression can be written as

`sin(2 cos^(-1)(7)/(25))`

`cos^(-1)(7)/(25)`= 73.739°

now sin(2\times73.739)= sin(147.47)

= 0.5377

therefore the exact value of the expression

`sin(2 cos^(-1)(7)/(25))`= 0.5377

please pay attention on each step, hope this helps.