Cosecant is 1 over sine. Secant is 1 over cosine. Cotangent is 1 over tangent, or adjacent over opposite. The three base ratios are in SOH-CAH-TOA.
Flip the fraction
If sin θ = 3/5, csc θ = 5/3. If the question wants sec and you have a right triangle, hypotenuse over adjacent. Tangent as sine over cosine still holds, in sin squared plus cos squared.
Common angle values are in trig values to memorize. Right-triangle trig as a set is in right triangle trigonometry.
The bottom line
Reciprocal means flip the base ratio. Do not mix up which one pairs with sine.
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