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Articles & Books From Trigonometry
Cheat Sheet / Updated 02-09-2023
Trigonometry is the study of triangles, which contain angles, of course. Get to know some special rules for angles and various other important functions, definitions, and translations. Sines and cosines are two trig functions that factor heavily into any study of trigonometry; they have their own formulas and rules that you’ll want to understand if you plan to study trig for very long.
Article / Updated 08-11-2022
Even though each trigonometry function is perfectly wonderful, being able to express each trig function in terms of one of the other five trig functions is frequently to your advantage. For example, you may have some sine terms in an expression that you want to express in terms of tangent, so that all the functions match, making it easier to solve the equation.
Article / Updated 08-10-2022
Even though each trigonometry function is perfectly wonderful, being able to express each trig function in terms of one of the other five trig functions is frequently to your advantage. For example, you may have some sine terms in an expression that you want to express in terms of cotangent, so that all the functions match, making it easier to solve the equation.
Article / Updated 12-21-2021
The relationship between the cosine and sine graphs is that the cosine is the same as the sine — only it’s shifted to the left by 90 degrees, or π/2. The trigonometry equation that represents this relationship isLook at the graphs of the sine and cosine functions on the same coordinate axes, as shown in the following figure.
Article / Updated 07-12-2021
One way to find the values of the trig functions for angles is to use the coordinates of points on a circle that has its center at the origin. Letting the positive x-axis be the initial side of an angle, you can use the coordinates of the point where the terminal side intersects with the circle to determine the trig functions.
Article / Updated 07-09-2021
The Pythagorean theorem states that a2 + b2 = c2 in a right triangle where c is the longest side. You can use this equation to figure out the length of one side if you have the lengths of the other two. The figure shows two right triangles that are each missing one side's measure.In the left triangle, the measure of the hypotenuse is missing.
Article / Updated 07-09-2021
There are several ways of drawing an angle in a circle, and each has a special way of computing the size of that angle. Four different types of angles are: central, inscribed, interior, and exterior. Here, you see examples of these different types of angles. Central angle A central angle has its vertex at the center of the circle, and the sides of the angle lie on two radii of the circle.
Article / Updated 07-07-2021
A circle is a geometric figure that needs only two parts to identify it and classify it: its center (or middle) and its radius (the distance from the center to any point on the circle). After you've chosen a point to be the center of a circle and know how far that point is from all the points that lie on the circle, you can draw a fairly decent picture.
Article / Updated 07-07-2021
The unit circle is a platform for describing all the possible angle measures from 0 to 360 degrees, all the negatives of those angles, plus all the multiples of the positive and negative angles from negative infinity to positive infinity. In other words, the unit circle shows you all the angles that exist.Because a right triangle can only measure angles of 90 degrees or less, the circle allows for a much-broader range.
Step by Step / Updated 03-27-2016
The graphs of the trig functions have many similarities and many differences. The graphs of the sine and cosine look very much alike, as do the tangent and cotangent, and then the secant and cosecant have similarities. But those three groupings do look different from one another. The one characteristic that ties them all together is the fact that they're periodic, meaning they repeat the same curve or pattern over and over again, in either direction along the x-axis.