What is the value of cos2x if sinx=1/3 ?
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Tushar Chandra
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We know that cos 2x = 1 - 2*(sin x)^2
we have sin x = 1/3
=> cos 2x = 1 - 2*(1/3)^2
=> cos 2x = 1 - 2*(1/9)
=> cos 2x = (9 - 2)/9
=> cos 2x = 7/9
The value of cos 2x = 7/9
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giorgiana1976 | Student
The problem requires the double angle identity:
cos 2x = 2 (cos x)^2 - 1
We'll determine cos x, applying the Pythagorean identity:
(cos x)^2 + (sin x)^2 = 1
(cos x)^2 = 1 - (sin x)^2
(cos x)^2 = 1 - 1/9
(cos x)^2 = (9-1)/9
(cos x)^2 = 8/9
We'll replace the value of (cos x)^2 into the double angle identity:
cos 2x = 2*8/9 - 1
cos 2x = (16-9)/9
cos 2x = 7/9
The value of cos 2x, if sin x = 1/3, is: cos 2x = 7/9.
Student Answers