How to Find Reference Angle in Quadrant 3? Therefore, the reference angle for 7π/6 is π/6. The calculation to find the reference angle of 7π/6 is given below: For example, the reference angle of -78° is 78°. If θ in a negative angle -θ is from 0 to 90 degrees, then its reference angle is θ. Therefore, 80° is the required reference angle of a negative angle of -1000°. For example, to find the reference angle of -1000°, we will add 360° three times to it. To find the reference angle of a negative angle, we have to add 360° or 2π to it as many times as required to find its coterminal angle. How to Find Reference Angle of Negative Angle? Follow the rules given below to find reference angles in radians: The only difference is that in radians we replace 180° by π and 360° by 2π. To find reference angles in radians is the same as finding them in degrees. It is always positive and cannot be negative in measurement. Can Reference Angles be Negative?Ī reference angle is a non-negative angle.
Thus, the reference angle of 200° is 20°. What is the Reference Angle for a 200° Angle?īetween the angles 180° and 360°, we can say that 200° is close to 180° by 20°. Therefore, 40° is the reference angle of 500°.
The first step is to find the coterminal angle of the given angle that lies between 0° to 360°.let's say of 500°, follow the steps given below: It is important to understand the reference angle as it has its applications in finding the values of trigonometric ratios and in representing trigonometric functions on graphs. It is a positive acute angle lies between 0° to 90° or a 90 degree angle. If we use reference angles, we don't need to remember the complete unit circle, instead we can just remember the first quadrant values of the unit circle.Ĭheck these interesting articles related to the concept of reference angles.įAQs on Reference Angle What is a Reference Angle?Ī reference angle is an angle bounded between the terminal arm and the x-axis.We have included the + sign because 135° is in quadrant II, where sine is positive. For example, we can see that the coterminal angle and reference angle of 495° are 135° and 45° respectively. We use the reference angle to find the values of trigonometric functions at an angle that is beyond 90°.The reference angle of any angle always lies between 0 and π/2 (both inclusive).The reference angle of an angle is always non-negative i.e., a negative reference angle doesn't exist.This is how we can find reference angles of any given angle. Thus, the reference angle of 480° is 60°. Step 3: The angle from step 2 is the reference angle of the given angle. Here, 120° does not lie between 0° and 90° and it is closest to 180° by 60°. If not, then we have to check whether it is closest to 180° or 360° and by how much. Step 2: If the angle from step 1 lies between 0° and 90°, then that angle itself is the reference angle of the given angle. We will subtract 360° from 480° to find its coterminal angle. Let's find the coterminal angle of 480° that lies between 0° and 360°. The coterminal angle can be found either by adding or subtracting 360° from the given angle as many times as required. Step 1: Find the coterminal angle of the given angle that lies between 0° and 360°. The steps to find the reference angle of an angle are explained with an example. But what if the given angle does not lie in this range? Let's see how we can find the reference angles when the given angle is greater than 360°. That table works only when the given angle lies between 0° and 360°. In the previous section, we learned that we could find the reference angles using the set of rules mentioned in the table.