Mindblown: a blog about philosophy.
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Trigonometric Ratios In 4 Quadrants
How to remember the signs of the trigonometric functions for the four quadrants?We can use a mnemonic like CAST or** A**ll** S**tudents **T**ake** C**alculus to remember the signs in the 4 quadrants. The following figure shows the signs of the trigonometric functions for the four quadrants. Scroll down the page for more examples and solutions. The trigonometric…
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How to Find Reference Angles?
In the previous section, we learned that we could find the reference angles using the set of rules mentioned in the table. That table works only when the given angle lies between 0° and 360°. But what if the given angle does not lie in this range? Let’s see how we can find the reference…
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Reference Angle
In math, a reference angle is generally an acute angle enclosed between the terminal arm and the x-axis. It is always positive and less than or equal to 90 degrees. Let us learn more about the reference angle in this article. Reference Angle Definition The reference angle is the smallest possible angle made by the terminal side of the…
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Imp. Notes on Coterminal Angles:
The difference (in any order) of any two coterminal angles is a multiple of 360° To find the coterminal angle of an angle, we just add or subtract multiples of 360°. from the given angle. The number of coterminal angles of an angle is infinite because there is an infinite number of multiples of 360°.…
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Coterminal Angles and Reference Angles
We already know how to find the coterminal angles of a given angle. The reference angle of any angle always lies between 0° and 90°, It is the angle between the terminal side of the angle and the x-axis. The reference angle depends on the quadrant’s terminal side. The steps to find the reference angle of an…
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Positive and Negative Coterminal Angles
The coterminal angles can be positive or negative. In one of the above examples, we found that 390° and -690° are the coterminal angles of 30° Here, 390° is the positive coterminal angle of 30° and -690° is the negative coterminal angle of 30° θ ± 360 n, where n takes a positive value when…
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How to Find Coterminal Angles?
From the above explanation, for finding the coterminal angles: add or subtract multiples of 360° from the given angle if the angle is in degrees. add or subtract multiples of 2π from the given angle if the angle is in radians. So we actually do not need to use the coterminal angles formula to find…
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Example
Find two coterminal angles of 30°. Solution: The given angle is, θ = 30° The formula to find the coterminal angles is, θ ± 360n Let us find two coterminal angles. For finding one coterminal angle: n = 1 (anticlockwise) Then the corresponding coterminal angle is, = θ + 360n= 30 + 360 (1)= 390°…
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Coterminal Angles Formula
The formula to find the coterminal angles of an angle θ depending upon whether it is in terms of degrees or radians is: Degrees: θ ± 360 n Radians: θ ± 2πn In the above formula, θ ± 360n, 360n means a multiple of 360, where n is an integer and it denotes the number of rotations around the coordinate plane.…
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Coterminal Angles
The coterminal angles are the angles that have the same initial side and the same terminal sides. We determine the coterminal angle of a given angle by adding or subtracting 360° or 2π to it. In trigonometry, the coterminal angles have the same values for the functions of sin, cos, and tan. Once you have…
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