1. Determine the quadrant in which the terminal side of the angle is found and find the corresponding reference angle.
theta = 4
I assume that Ø = 4 radians
2π radians = appr 6.28
3π/2 = 4.7
π rad = 3.14
so 4 radians must be in quadrant III
and the reference angle is 4 - π = .8584
check: since in III the tangent is positive,
tan 4 = 1.1578
tan .8584 = 1.155 , close enough
thankyou!
To determine the quadrant in which the terminal side of the angle is found, we first need to find the standard position of the angle.
Given that theta = 4, we know that the angle is positive and lies in the first quadrant (0 to 90 degrees or 0 to π/2 radians).
To find the corresponding reference angle, we subtract the given angle from 90 degrees (or π/2 radians) since reference angles are always measured in relation to the nearest x-axis.
Reference angle = 90 - theta = 90 - 4 = 86 degrees (or π/2 - 4 radians).
To determine the quadrant in which the terminal side of the angle is found and to find the corresponding reference angle, you need to consider the value of the angle theta.
In this case, theta = 4.
To find the quadrant, you can divide the angle range (0 to 360 degrees or 0 to 2π radians) into four equal parts:
1. Quadrant I: 0 to 90 degrees or 0 to π/2 radians
2. Quadrant II: 90 to 180 degrees or π/2 to π radians
3. Quadrant III: 180 to 270 degrees or π to 3π/2 radians
4. Quadrant IV: 270 to 360 degrees or 3π/2 to 2π radians
Since the angle theta = 4 lies between 0 and 90 degrees or 0 and π/2 radians, the terminal side of the angle is found in Quadrant I.
To find the corresponding reference angle, you subtract the given angle theta from 90 degrees or π/2 radians:
Reference angle = 90 degrees - theta = 90 - 4 = 86 degrees
Or,
Reference angle = π/2 radians - theta = π/2 - 4 ≈ 0.14 radians
Therefore, the terminal side of the angle theta = 4 is found in Quadrant I, and the corresponding reference angle is 86 degrees or approximately 0.14 radians.