Question

The expression cosine of pi over 2 times cosine of pi over 5 plus sine of pi over 2 times sine of pi over 5 can be rewritten as which of the following?
cosine of 7 times pi over 10
cosine of 3 times pi over 10
sine of 7 times pi over 10
sine of 3 times pi over 10


(The clear version of the question is in the picture below)

Answer 1

Answer:

  (b)  cos(3π/10)

Step-by-step explanation:

The given expression matches the trig identity form for the cosine of the difference of two angles:

  cos(α-β) = cos(α)cos(β) +sin(α)sin(β)

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To match the given expression exactly, we can choose ...

  α = π/2

  β = π/5

Then the difference is ...

  α -β = π/2 -π/5 = (5/10)π -(2/10)π = 3π/10

The given expression can be shortened to ...

  cos(3π/10)

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Additional comment

Sometimes it can be difficult to remember when the signs in trig identities match, and when they differ. The fact that cosines of smaller angles have larger values can be a peg on which to hang that hat.