To simplify sin(π/2 – θ), we can use a fundamental identity from trigonometry known as the co-function identity. The identity states that:
sin(π/2 – θ) = cos(θ)
This means that the sine of an angle subtracted from π/2 is equal to the cosine of that angle. Therefore, in this case:
sin(π/2 – θ) = cos(θ)
This simplification can be particularly useful when solving trigonometric equations or trying to evaluate specific angles. For example, if θ is a specific angle like 30 degrees (or π/6 radians), you can easily calculate:
- sin(π/2 – π/6) = cos(π/6)
- cos(π/6) = √3/2
So, the process of simplifying sin(π/2 – θ) directly leads us to the cosine function, making calculations more straightforward.