NECO 2008 Mathematics · Question 14

Find y if sin y = cos 48°

Options

A.21°
B.24°
C.42°
D.48°
E.102°

Answer: C. 42°

Explanation written with AI and checked against the answer key

Analyze the question: We need an angle y such that sin y = cos 48°. This uses the complementary angle relationship. Concept: For complementary angles (angles that add up to 90°): sin θ = cos(90° − θ) So sin y = cos 48° means y and 48° are complementary. Solution: sin y = cos 48° Since cos 48° = sin(90° − 48°) = sin 42°, sin y = sin 42° so y = 42° Check: sin 42° ≈ 0.6691 and cos 48° ≈ 0.6691, so they match. (Note: sin y = sin(180° − 42°) also gives 138°, but that is not among the options, so 42° is the answer.) Tip: "Sine and cosine of complementary angles are equal." If you see sin y = cos x, just use y = 90° − x. The name "cosine" literally means "complement's sine."

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