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: $-\dfrac{2\sqrt{14}}{9}$

Step-by-step explanation:

Given

$\cos a=\dfrac{5}{9}$

$a$ 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

$\Rightarrow \sin^2 a=1-\dfrac{5^2}{9^2}$

$\\\\\Rightarrow \sin^2 a=1-\dfrac{25}{81}\\\\\\\Rightarrow \sin^2 a=\dfrac{56}{81}\\\\\\\Rightarrow \sin a=-\sqrt{\dfrac{56}{81}}\\\\\\\Rightarrow \sin a=-\dfrac{2\sqrt{14}}{9}$