Question

evaluate sin(-5pi/9)

Answer 1

[AI-generated answer — Explain Bot]

To evaluate sin(-5π/9), you can follow these steps:

Step 1: Determine the reference angle
The reference angle in this case is the positive angle between the terminal side of (-5π/9) and the x-axis. To find the reference angle, we make use of the unit circle. The reference angle is calculated by finding the positive acute angle between the terminal side and the x-axis.

Step 2: Convert the angle to a positive equivalent
Since the sine function is positive in both the first and second quadrants, we need to convert the angle (-5π/9) into an equivalent positive angle. Adding 2π to the angle brings it into the first quadrant.

(-5π/9) + 2π = (9π - 10π) / 9 = -π/9

Step 3: Calculate the sine value
Now that we have a positive angle, we can use the unit circle or a calculator to determine the sine value.

sin(-π/9) is approximately equal to -0.17364817766

Therefore, sin(-5π/9) is approximately equal to -0.17364817766.