Yes, sin(0) is indeed equal to cos(90), and here’s why.
In trigonometry, the sine and cosine functions are related to the angles in a right triangle. Specifically:
- sin(0) represents the sine of 0 degrees, which is the ratio of the opposite side to the hypotenuse in a right triangle. Since there is no opposite side at 0 degrees, sin(0) equals 0.
- cos(90) represents the cosine of 90 degrees, which is the ratio of the adjacent side to the hypotenuse. At 90 degrees, there is no adjacent side, and thus, cos(90) is also 0.
Therefore, both sin(0) and cos(90) equal 0, making them equal to each other. This is a fundamental property of the sine and cosine functions due to their definitions on the unit circle, where:
- At 0 degrees, the point on the unit circle is (1, 0), leading to sin(0) = 0.
- At 90 degrees, the point is (0, 1), leading to cos(90) = 0.
In conclusion, sin(0) = 0 and cos(90) = 0. Thus, they are equal.