To understand why cos(90) * sin(x) and sin(90) * cos(x) yield specific results, we first need to look at the trigonometric values of the angles involved.
1. **Trigonometric Values**: The cosine of 90 degrees is zero, while the sine of 90 degrees is one:
cos(90) = 0sin(90) = 1
2. **Calculating the Expressions**:
– For cos(90) * sin(x): This simplifies to 0 * sin(x) = 0. This means that no matter the value of sin(x), the entire expression equals zero because multiplying by zero yields zero.
– For sin(90) * cos(x): This simplifies to 1 * cos(x) = cos(x). Here, the value of sin(90) is one, which means the expression retains the original value of cos(x).
3. **Understanding in Context**: These relationships are indicative of the fundamental properties of sine and cosine functions in trigonometry. The unit circle allows us to visualize these functions, where:
- At 90 degrees, the point on the unit circle is (0, 1), indicating that the cosine value (x-coordinate) is zero and the sine value (y-coordinate) is one.
- When dealing with these operations, we can observe how sin and cos relate to each other at specific angles, and how multiplying them by sine or cosine of 90 degrees will impact their values.
In conclusion, the expressions cos(90) * sin(x) and sin(90) * cos(x) reflect foundational trigonometric principles, with one yielding zero and the other returning the cosine of the angle x.