Find the Exact Value (cos(10))/(sin(80))

Problem

cos(10)/sin(80)

Solution

1. Identify the relationship between the angles in the numerator and the denominator. Note that 10 and 80 are complementary angles because 10+80=90

2. Apply the cofunction identity which states that sin(θ)=cos(90−θ)

3. Substitute θ=80 into the identity to rewrite the denominator.

sin(80)=cos(90−80)

4. Simplify the expression inside the cosine function.

sin(80)=cos(10)

5. Substitute this result back into the original fraction.

cos(10)/sin(80)=cos(10)/cos(10)

6. Divide the numerator by the denominator. Since any non-zero value divided by itself is 1 the expression simplifies to 1

Final Answer

cos(10)/sin(80)=1

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