In trigonometry, trigonometric identities are equalities that involve trigonometric functions and are true for every value of the occurring variables for which both sides of the equality are defined. Geometrically, these are identities involving certain functions of one or more angles .

The three main functions in trigonometry are Sine, Cosine and Tangent. They are just the length of one side divided by another. For a right triangle with an angle θ:

Trigonometry helps us find angles and distances, is used a lot in science, engineering, video games, and more! The triangle of most interest is the right-angled triangle. The right angle is shown by the little box in the corner: Another angle is often labeled θ, and the three sides are then called: Why a Right-Angled Triangle?

正弦函数的图是美丽的波浪形曲线（每 2 π 弧度（360°）重复一遍）。 图从 0 开始，在 π /2 弧度（90°）上升到 1，然后降回 -1。 余弦和正弦一样，但图从 1 开始，下降到角的值为 π 弧度 （180°），然后再上升. 正弦和余弦就像 好朋友：一个跟着另一个，隔开的距离是刚好 " π /2" 弧度（90°）。 正切的图有完全不同的形状……它处于正与负 无穷大 之间，每 π 弧度（180°）经过 0 一次，像这样： 在 π /2 弧度（90°），和 - π /2、3 π /2 等等，正切函数是 未定义的，因为它 …

Solution of the simplest trigonometric equations: sin(x) = a ⇔ x = (-1) n arcsin(a) + n π, n = 0, 1 ... ∈ Z cos(x) = a ⇔ x = ± arccos(a) + 2 n π, n = 0, 1 ... ∈ Z

Trigonometric functions are functions related to an angle. There are six trigonometric functions: sine, cosine, tangent and their reciprocals cosecant, secant, and cotangent, respectively. Sine, cosine, and tangent are the most widely used trigonometric functions. Their reciprocals, though used, are less common in modern mathematics.

Quadrant rule to solve trig equations; Using the identities: tanθ ≡sinθ/cosθ and sin²θ+cos²θ ≡1

Trigonometric functions allow us to use angle measures, in radians or degrees, to find the coordinates of a point on any circle—not only on a unit circle—or to find an angle given a point on a circle. They also define the relationship between the sides and angles of a triangle.

2020年12月21日 · Quotient and reciprocal identities \[\tan\theta=\dfrac{\sin\theta}{\cos\theta}\] \[\cot\theta=\dfrac{\cos\theta}{\sin\theta}= \dfrac{\csc\theta}{\sec\theta}= \dfrac{1 ...

We review the properties of trigonometric functions. Topics. 5.1 Definition of Sine and Cosine and their Graphs. 5.2 Basic Properties. 5.3 Additional Definitions. 5.4 Further Properties. 5.5 Differential Properties. 5.6 The Law of Sines. 5.7