Question

If angle a has the terminal ray that falls in the fourth quadrant and cosine a equals 5/9 then determine the value of sin a in simplest radical form

Answer 1

Answer:
`-(2√(14))/(9)`

Explanation:

Given

`\cos a=(5)/(9)`

`a` lies in the fourth quadrant

So, sine must be negative in the fourth quadrant

Using identity
`\sin ^2 x+\cos^2 x=1` to find sine value

`\Rightarrow \sin^2 a=1-(5^2)/(9^2)`

`\\\\\Rightarrow \sin^2 a=1-(25)/(81)\\\\\\\Rightarrow \sin^2 a=(56)/(81)\\\\\\\Rightarrow \sin a=-\sqrt{(56)/(81)}\\\\\\\Rightarrow \sin a=-(2√(14))/(9)`