Find the reference angle θ'.
θ= -7pi/9
-7pi/9 + 2pi = 11pi/9
This is in QII, so we need to subtract it from pi:
pi - 11pi/9 = 7pi/9
You can also subtract 2pi if the angle is large and positive.
Oops. 11pi/9 > pi, so subtract pi to get
2pi/9
play around adding and subtracting 2pi or pi till you get an angle in QI.
To find the reference angle θ', you need to determine the acute angle formed between the terminal side of angle θ and the x-axis.
Step 1: Find the positive equivalent angle.
Since θ is negative, you can find the positive equivalent angle by adding 2π (or 360 degrees) to θ.
θ = -7π/9
θ' = -7π/9 + 2π = 5π/9
Step 2: Calculate the reference angle.
The reference angle is the acute angle formed between the terminal side of θ and the x-axis. Since θ' is already positive, the reference angle is θ'.
Therefore, the reference angle is θ' = 5π/9.
To find the reference angle θ', we need to find the acute angle formed by the terminal side of the angle θ and the x-axis.
In this case, θ = -7pi/9. To determine the reference angle, follow these steps:
1. Find the equivalent positive angle: Since the angle is negative, we add 2π (or 360 degrees) to get the equivalent positive angle.
θ_eq = θ + 2π = -7pi/9 + 2pi = (5pi/9)
2. Subtract π (or 180 degrees) from the equivalent positive angle:
θ' = θ_eq - π = (5pi/9) - pi
To make it easier for comparison, let's express both terms with a common denominator:
θ' = (5pi/9) - (9pi/9) = -4pi/9
Therefore, the reference angle θ' for θ = -7pi/9 is -4pi/9.