Given cosalpha=1/3, how do you find sinalpha?

2 Answers
Azimet
Jan 15, 2017

sin(a) = +-(2sqrt2)/3

Explanation:

You can use a trig identity that states that cos^2(a) = 1 - sin^2(a)

so we get that

1/9 = 1 - sin^2(a) => sin^2(a) = 8/9 => sin(a) = +-(2sqrt2)/3

Douglas K.
Jan 15, 2017

Use the identity cos^2(alpha) + sin^2(alpha) = 1 and solve for sin(alpha):

sin(alpha) = +-sqrt(1 - cos^2(alpha))

Explanation:

Substitute (1/3)^2 for cos^2(alpha)

sin(alpha) = +-sqrt(1 - (1/3)^2)

sin(alpha) = +-sqrt(1 - 1/9)

sin(alpha) = +-sqrt(8/9)

sin(alpha) = +-sqrt(8)/3

sin(alpha) = +-(2sqrt(2))/3

Because we are not given any clue whether alpha is in the first or the fourth quadrant, then we cannot determine whether the sine function is positive or negative.

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