Question

If cos(t) = 2/7 and t is in the 4th quadrant, find sin(t).

Answer 1

We can use the Pythagorean Trigonometric Identity which says:
$sin^2(t)+cos^2(t)=1$

Since we need to find sin(t), we have to solve for it:
$sin(t)= \sqrt{1-cos^2(t)}$

Let's plug in the given cos(t) value:
$sin(t) = \sqrt{1-cos^2( \frac{2}{7})}$

And solve sin(t):
$sin(t) = \sqrt{1- \frac{4}{49} } = \frac{x}{y} \sqrt{ \frac{49}{49}- \frac{4}{49} }$

Simplify further:
$sin(t) = \sqrt{ \frac{45}{49} } = \frac{ \sqrt{45} }{7} = \frac{ \sqrt{9*5} }{7}$

And it all simplifies down to:
$sin(t) = \frac{3 \sqrt{5} }{7}$

Since it's in the 4th quadrant, the sin(t) value is going to be negative. So, your final answer is: 
$sin(t) = - \frac{ 3\sqrt{5} }{7}$

Hope this helps!