Calculate the reference angle for 150°
Reference Angle = A postive, acute angle.
0 ≤ θ ≤ 90°
Step 1: Find equivalent angle
Our original angle fits:
0° ≤ 150° ≤ 360°
Step 2: Determine the quadrant:
| 2 | 1 |
| 3 | 4 |
150° is located in Quadrant II
Reference Angle = 180° - 150
Step 3: Find the reference angle:
| Quadrant | Reference angle for θ |
| 1 | θ |
| 2 | 180 - θ |
| 3 | θ - 180 |
| 2 | 360 - θ |
Reference Angle = 30°
You have 2 free calculationss remaining
What is the Answer?
Reference Angle = 30°
How does the Reference Angle Calculator work?
Free Reference Angle Calculator - Calculates the reference angle for a given angle. Also known as the positive acute angle.
This calculator has 1 input.
This calculator has 1 input.
What 4 formulas are used for the Reference Angle Calculator?
Quadrant 1 = θ
Quadrant 2 = 180 -θ
Quadrant 3 = θ - 180
Quadrant 4 = 360 - θ
For more math formulas, check out our Formula Dossier
Quadrant 2 = 180 -θ
Quadrant 3 = θ - 180
Quadrant 4 = 360 - θ
For more math formulas, check out our Formula Dossier
What 10 concepts are covered in the Reference Angle Calculator?
- angle
- the figure formed by two rays, called the sides of the angle, sharing a common endpoint, called the vertex of the angle.
- cos
- cos(θ) is the ratio of the adjacent side of angle θ to the hypotenuse
- cot
- The length of the adjacent side divided by the length of the side opposite the angle. Also equals 1/tan(θ)
- csc
- the length of the hypotenuse divided by the length of the adjacent side. Also equals 1/sin(θ)
- gradian
- defined as one hundredth of the right angle. This is equal to π/200 or 9/10°
- radian
- a unit of plane angular measurement that is equal to the angle at the center of a circle subtended by an arc whose length equals the radius or approximately 180°/π ~ 57.3 degrees.
- reference angle
- the smallest possible angle made by the terminal side of the given angle with the x-axis.
- sec
- the length of the hypotenuse divided by the length of the adjacent side. Also equals 1/cos(θ)
- sin
- sin(θ) is the ratio of the opposite side of angle θ to the hypotenuse
- tan
- the ratio of the opposite side to the adjacent side of a particular angle of the right triangle.
Example calculations for the Reference Angle Calculator
Reference Angle Calculator Video
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