The reciprocal relationship for sine and cosecant is which of the following?

The reciprocal relationship for sine and cosecant is which of the following?

• A. Sine and Cosecant
• B. Sine and Tangent
• C. Cosecant and Tangent
• D. Cosine and Sine

Answer: (A)

The idea being tested is how sine and cosecant relate as reciprocal functions. Sine is defined as opposite over hypotenuse. Cosecant is defined as hypotenuse over opposite. Because these are flipped, they are reciprocals: csc θ = 1/(sin θ) and sin θ = 1/(csc θ). A quick example helps: if sin θ = 1/3, then csc θ = 3. Note that when sin θ is zero, csc θ isn’t defined, but wherever sine is nonzero, they are exact reciprocals. The other pairings aren’t reciprocal relations (cosine’s reciprocal is secant; tangent’s reciprocal is cotangent), so the sine–cosecant relationship is the one that fits.

The idea being tested is how sine and cosecant relate as reciprocal functions. Sine is defined as opposite over hypotenuse. Cosecant is defined as hypotenuse over opposite. Because these are flipped, they are reciprocals: csc θ = 1/(sin θ) and sin θ = 1/(csc θ). A quick example helps: if sin θ = 1/3, then csc θ = 3.

Note that when sin θ is zero, csc θ isn’t defined, but wherever sine is nonzero, they are exact reciprocals. The other pairings aren’t reciprocal relations (cosine’s reciprocal is secant; tangent’s reciprocal is cotangent), so the sine–cosecant relationship is the one that fits.