Find the Complement cos(75)

Problem

cos(75)

Solution

1. Identify the cofunction identity for cosine, which states that the cosine of an angle is equal to the sine of its complement.

cos(θ)=sin(90−θ)

2. Substitute the given angle θ=75 into the identity.

cos(75)=sin(90−75)

3. Subtract the values inside the parentheses to find the complementary angle.

90−75=15

4. State the resulting trigonometric expression.

cos(75)=sin(15)

Final Answer

cos(75)=sin(15)

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