Given $\sin 58° = \cos p°$, find p.

Analysis

The question asks us to find the value of $p$ given the equation $\sin 58° = \cos p°$. This is a classic trigonometry problem involving the relationship between complementary angles.

Concept: Complementary Angles

In trigonometry, the sine and cosine functions are "cofunctions." This means that the sine of an angle is equal to the cosine of its complement. The complement of an angle $\theta$ is $(90° - \theta)$.

The fundamental identity is:

or conversely:

Step-by-Step Solution

1. Identify the given equation: $\sin 58° = \cos p°$

2. Apply the identity: We know that $\sin \theta = \cos(90° - \theta)$. Substituting $58°$ for $\theta$: $\sin 58° = \cos(90° - 58°)$

3. Simplify the expression: $90° - 58° = 32°$ Therefore, $\sin 58° = \cos 32°$

4. Compare with the given equation: Since $\sin 58° = \cos p°$ and we found $\sin 58° = \cos 32°$, it follows that: $p = 32$

Conclusion

Comparing our result with the options provided, we see that $p = 32°$ corresponds to option C.

Exam Tip

Whenever you see $\sin x = \cos y$ in a JAMB question, simply remember that $x + y$ must equal $90°$. In this case: $58° + p° = 90° \implies p = 90° - 58° = 32°$. This shortcut will save you valuable time during the exam!