# 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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### 1 Answer

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` .**