To solve this trigonometric problem, we need to use the fact that the sine of an angle and the cosine of its complement are equal. That is, if x is an acute angle, then:
sin(x) = cos(90° - x)
Using this identity, we can rewrite the given equation:
sin(58°) = cos(p°)
cos(90° - 58°) = cos(p°) (using the identity)
cos(32°) = cos(p°) (simplifying)
Now, since the cosine function is periodic with a period of 360°, any two angles whose cosine values are equal must differ by a multiple of 360°. That is:
p° = 32° + 360°n (where n is an integer)
So, there are infinitely many possible values of p° that satisfy the equation. Some examples are:
p° = 32° (n = 0)
p° = 392° (n = 1)
p° = -328° (n = -1)
Note that we can find these values by adding or subtracting multiples of 360° to the initial value of 32°, since the cosine function has the same value for an angle and its coterminal angles.