Given that sin A = 1/3 and angle A is in the first quadrant, find cos A
2 answers:
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 answer: 2√2 / 3
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