Question

question 24 (multiple choice worth 1 points)
(05.02r lc)

which pair of angles has congruent values for the \\(\sin x^{\circ}\\) and the \\(\cos y^{\circ}\\)?

\\(42^{\circ}; 42^{\circ}\\)
\\(42^{\circ}; 48^{\circ}\\)
\\(42^{\circ}; 138^{\circ}\\)
\\(42^{\circ}; 132^{\circ}\\)

Explanation:

Apply the cofunction identity

$$ \sin(x^\circ) = \cos(90^\circ - x^\circ) $$

Relate the angles

$$ y^\circ = 90^\circ - x^\circ \implies x^\circ + y^\circ = 90^\circ $$

Test the given options

$$ 42^\circ + 48^\circ = 90^\circ $$

Answer:

• (A) \(42^\circ; 42^\circ\)
• (B) \(42^\circ; 48^\circ\) (Correct answer)
• (C) \(42^\circ; 138^\circ\)
• (D) \(42^\circ; 132^\circ\)