The Pythagoras theorem states that if a triangle is right-angled (90 degrees), then the square of the hypotenuse is equal to the sum of the squares of the other two sides. Observe the following triangle ABC, in which we have BC2 = AB2 + AC2. Here, AB is the base, AC is the altitude (height), and BC is the hypotenuse. It is to… Continue reading What is the Pythagoras Theorem?
Month: September 2022
Introduction
Pythagoras Theorem : The Pythagoras theorem which is also referred to as the Pythagorean theorem explains the relationship between the three sides of a right-angled triangle. According to the Pythagoras theorem, the square of the hypotenuse is equal to the sum of the squares of the other two sides of a triangle. Let us learn more about… Continue reading Introduction
Unit Circle and Trigonometric Values
The various trigonometric identities and their principal angle values can be calculated through the use of a unit circle. In the unit circle, we have cosine as the x-coordinate and sine as the y-coordinate. Let us now find their respective values for θ = 0°, and θ = 90º. For θ = 0°, the x-coordinate… Continue reading Unit Circle and Trigonometric Values
Unit Circle and Trigonometric Identities
The unit circle identities of sine, cosecant, and tangent can be further used to obtain the other trigonometric identities such as cotangent, secant, and cosecant. The unit circle identities such as cosecant, secant, cotangent are the respective reciprocal of the sine, cosine, tangent. Further, we can obtain the value of tanθ by dividing sinθ with… Continue reading Unit Circle and Trigonometric Identities
Unit Circle with Sin Cos and Tan
Any point on the unit circle has coordinates(x, y), which are equal to the trigonometric identities of (cosθ, sinθ). For any values of θ made by the radius line with the positive x-axis, the coordinates of the endpoint of the radius represent the cosine and the sine of the θ values. Here we have cosθ = x,… Continue reading Unit Circle with Sin Cos and Tan
Equation of a Unit Circle
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… Continue reading Equation of a Unit Circle
Unit Circle
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… Continue reading Unit Circle
Trig. Functions in the Cartesian Plane
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… Continue reading Trig. Functions in the Cartesian Plane
Finding the Quadrant in Which an Angle Lies
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… Continue reading Finding the Quadrant in Which an Angle Lies
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… Continue reading Trigonometric Ratios In 4 Quadrants