Simplify sin(65)

Problem

sin(65^∘)

Solution

1. Identify the expression as the sine of an angle measured in degrees.

2. Determine if the angle is a standard reference angle (such as 0^∘ 30^∘ 45^∘ 60^∘ or 90^∘.

3. Conclude that since 65^∘ is not a standard reference angle, the expression sin(65^∘) is already in its simplest exact radical form. It can also be expressed in terms of its cofunction, the cosine of the complementary angle.

4. Apply the cofunction identity sin(θ)=cos(90^∘−θ)

5. Calculate the complement: 90^∘−65^∘=25^∘

Final Answer

sin(65^∘)=cos(25^∘)

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