For what value of x is cos(x) = sin(14°), where 0° < x < 90°?
Since cos(x) = sin(90° - x) for 0° < x < 90°, we have:
cos(x) = sin(14°)
cos(x) = sin(90° - 14°)
cos(x) = sin(76°)
Since the cosine function is decreasing on this interval, we can find the value of x by finding when sin(76°) is at its maximum value.
From the unit circle, we know that the maximum value of sin(76°) is 1.
Therefore, we have:
cos(x) = 1
Since 0° < x < 90°, the only possible value for x is x = 0°.
Thus, the value of x such that cos(x) = sin(14°) is x = 0°.