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Let(theta) be in Q3, cos(theta) = -5/3, find cos2(theta) and determine in which...

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rapsplash | Student, Undergraduate | eNoter

Posted May 5, 2012 at 6:26 PM via web

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Let(theta) be in Q3, cos(theta) = -5/3, find cos2(theta) and determine in which quadrant 2(theta) terminates. Draw 2 diagrams.

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sciencesolve | Teacher | (Level 3) Educator Emeritus

Posted May 5, 2012 at 7:10 PM (Answer #1)

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You need to use the following formula for cosine of double angle such that:

`cos 2 theta = 2 cos^2 theta - 1`

You need to substitute `-5/3`  for cos theta such that:

`cos 2 theta = 50/9 - 1`

You need to bring the terms to a common denominator such that:

`cos 2 theta = (50-9)/9`

`cos 2 theta = 41/9`

Notice that there is no such a  value for angle `2 theta ` for `cos 2 theta = 41/9gt1`  as there is no such a value for `theta`  such that `cos theta = -5/3 gt 1` .

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