Given that sin a = 1/3 and angle a is in the first quadrant, find cos a

Sin A = opposite / hypotenuse 

If angle A is in the first quadrant, that means both x and y coordinate are positive.

Now you can draw triangle. Since sinA = 1/3, opposite side may be 1, so then hypotenuse side must be 3.

Now you can use Pythagorean Theorem to solve for the length of adjacent side:

a² + b² = c²
1 + b² = 9
b² = 8
b = 2√2

So adjacent side is 2√2.

So now we can solve for cosA:

cosA = adjacent / hypotenuse = 2√2 / 3

Final 2√2 / 3