Math CentralQuandaries & Queries


Question from meisje, a student:

sin105degree + sin15degree
Can you show me the steps and how to find the exact value?

Hi there.

The steps are basically to recall what exact values you know: 0, 30, 45, 60, 90. Then recall that you have trig identities allowing you to use "sum" and "difference", "double" and "half" angles.

Cos(15) = Cos(30/2) so I would look for a Cos(θ/2) form.

Cos(15) = Cos(30/2) = Sqrt[ (1 + Cos 30) / 2 ]

and now I can substitute in the exact value of Cos 30 and simplify.

Cos(105) = Cos (90 + 15). So I'd first find a Cos(θ + φ) identity.

Cos(105) = Cos(90) Cos(15) - Sin(90) Sin(15) = -Sin(15)

and then I'd use the same idea to solve -Sin(15).

This strategy should work for you. Just combine the steps and calculate your question: Sin 105 + Sin 15.

Stephen La Rocque.

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