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Author: misamaliraza94

  • Equation of a Unit Circle

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    The general equation of a circle is (x – a)2 + (y – b)2 = r2, which represents a circle having the center (a, b) and the radius r. This equation of a circle is simplified to represent the equation of a unit circle. A unit circle is formed with its center at the point(0, 0), which…

  • Unit Circle

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    misamaliraza94
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    A unit circle from the name itself defines a circle of unit radius. A circle is a closed geometric figure without any sides or angles. The unit circle has all the properties of a circle, and its equation is also derived from the equation of a circle. Further, a unit circle is useful to derive…

  • Trig. Functions in the Cartesian Plane

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    misamaliraza94
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    In these lessons, we will look at Trigonometric Functions for any angle in the Cartesian Plane by using the reference angle. Steps to solving trigonometric functions for any angle Step 1: Find the Reference Angle, which is always acuteStep 2: Find Trig Function Value for the reference angleStep 3: Determine the Sign (positive or negative) of the trig function…

  • Finding the Quadrant in Which an Angle Lies

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    misamaliraza94
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    An angle is said to be in standard position if its vertex is at the origin and its initial side is along the positive x-axis. An angle is said to be in the first quadrant, if in the standard position, its terminal side falls in the first quadrant. Similarly, we can define for the other…

  • Trigonometric Ratios In 4 Quadrants

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    misamaliraza94
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    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…

  • How to Find Reference Angles?

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    misamaliraza94
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    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…

  • Reference Angle

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    misamaliraza94
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    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…

  • Imp. Notes on Coterminal Angles:

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    misamaliraza94
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    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°.…

  • Coterminal Angles and Reference Angles

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    misamaliraza94
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    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…

  • Positive and Negative Coterminal Angles

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    misamaliraza94
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    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…