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JAMB Mathematics 2018 Paper

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Question : 44

Total: 62

Given that Sin (5

_{x}

^{\circ}

_{x}

^{\circ}

^{\circ}

Find the value of x

14 $^{\circ}$
21 $^{\circ}$
32 $^{\circ}$
39 $^{\circ}$

Solution:

Concept:

Use the complementary angle identity:

\sin \theta = \cos(90^{\circ} - \theta)

.

Explanation:

Given

\sin(5x - 28)^{\circ} = \cos(3x - 50)^{\circ}

.

Rewrite the left side using the identity:

\sin(5x - 28)^{\circ} = \cos(90^{\circ} - (5x - 28)^{\circ})

= \cos(90^{\circ} - 5x^{\circ} + 28^{\circ})

= \cos(118^{\circ} - 5x^{\circ})

.

Now equate the cosine expressions:

\cos(3x - 50)^{\circ} = \cos(118 - 5x)^{\circ}

So,

3x - 50 = 118 - 5x

.

Collect like terms:

3x + 5x = 118 + 50

8x = 168

x = \frac{168}{8} = 21^{\circ}

.

Answer:

x = 21^{\circ}

, which is option B.

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