Final answer:
The question refers to cofunction relationships in trigonometry which allows us to convert a cosine angle to a sine angle. The cosine angle, cos(5π/9), can be written as sin(π/2 - 5π/9), which simplifies to sin(4π/9)
Step-by-step explanation:
The equation you're referring to is an example of cofunction relationships in trigonometry, specifically about the cosine function. We can write any cosine function in terms of sine with a phase difference of 90°, because the sine and cosine are essentially the same function but shifted by 90°, also known as π/2 radians.
Therefore, using the relationship that cos(π/2 - θ) = sin(θ), we can write cos(5π/9) as sin(π/2 - 5π/9). After we simplify, it translates to sin(4π/9). That matching angle in sine demonstrates the cofunction relationship between sine and cosine.
Learn more about Cofunction Relationships