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Calculus/functions and identities

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Expert: - 12/11/2009


Question
Hi! I am preparing for a placement exam to go back to school and i am in the process of working out the practice questions. One of them is "If 0 degrees < x degrees < 90 degrees and sin x = 1/2 then cosine x= ??"  I only have the internet to help me and i cant find anything that relates please help

Answer
Since sin(x) is (length of the far side)/(length of the hypoteneuse),
that means the far side has length 1 and the hypoteneuse has length 2.

Now the law of squares for a triangle states that a² + b² = c².  We know b = 1 and c = 2.
Thus, the eqation is a² + 1 = 3, so a = √3.

The cos(x) s then √3/2.

Calculus

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