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given sin0= 2/3 and angle 0 is in quadrant 2, what is the exact value of cos0 in simplest form? simplify all radicals if needed

1 Answer

9 votes

Answer: ( -
√(5) / 3)

Explanation:

sin(angle) = opposite/hypotenuse

opposite =2

hypotenuse = 3

solve for adjacent side with pythagorean theorum

opposite^2 + adjacent^2 = hypotenuse^2

2^2 + adjacent^2 = 3^2

4 + adjacent^2 = 9

adjacent^2 = 9 - 4

adjacent^2 = 5

adjacent =
√(5)

-
√(5) since it is in the second quadrant

cosx = (adjacent/hypotenuse)

cosx = (-
√(5)/3)

(-
√(5)/3)

User Ankit Singhal
by
6.7k points
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