在三角函数中，csc（余割）和sec（正割）是余弦函数和正弦函数的倒数。它们与常见的三角函数sin（正弦）、cos（余弦）和tan（正切）之间存在以下关系： csc(x) = 1/sin(x) sec(x) = 1/cos(x) 其中，x表示角度。 2. 知识点运用： csc和sec函数是三角函数领域中常用的倒数 ...

\sec x = \frac{1}{\cos{x}} \csc{x} = \frac{1}{\sin{x}} \cot{x} = \frac{1}{\tan{x}} 平方关系 \sin^{2}x + \cos^{2}x = 1. 1 + \tan^{2} x = \sec^{2}x. 1 + \cot^{2}x = \csc^{2}x. 商关系 \tan{x} = \frac{\sin{x}}{\cos{x}} = \frac{\sec{x}}{\csc{x}} \cot{x} = \frac{\cos{x}}{\sin{x}} = \frac{\csc{x}}{\sec{x}} 三角恒等变换公式 和差公式

When the height and base side of the right triangle are known, we can find out the sine, cosine, tangent, secant, cosecant, and cotangent values using trigonometric formulas. The reciprocal trigonometric identities are also derived by using the trigonometric functions.

Secant, cosecant and cotangent, almost always written as sec, cosec and cot are trigonometric functions like sin, cos and tan. Note, sec x is not the same as cos -1 x (sometimes written as arccos x). Remember, you cannot divide by zero and so these definitions are only valid when the denominators are not zero. Example.

For sin, cos and tan the unit-length radius forms the hypotenuse of the triangle that defines them. The reciprocal identities arise as ratios of sides in the triangles where this unit line is no longer the hypotenuse. The triangle shaded blue illustrates the identity , and the red triangle shows that .

比如sin和cos. 我们会看到六边形的中心有个1. 所以我们会想到sin^2+cos^2=1. 也正是最上面的阴影三角形. 类似的，就有tan^2+1=sec^2，cot^2+1=csc^2. 这个大家能联想到什么呢？ 我想到的是杨辉三角. 图8 杨辉三角. 说白了，就是由两个肩上扛的数得到下面那个数. 我觉得 ...

2022年8月17日 · 正弦 （sine）, 余弦 （cosine） 和 正切 （tangent） （英语符号简写为 sin, cos 和 tan) 是 直角三角形 边长的比：对一个特定的角θ来说，不论三角形的大小，这三个比是不变的sec(θ) = 斜边 / 邻边(=1/cos)csc(θ) = 斜边 / 对边(=1/sin)cot(θ) = 邻边 / 对边(=1/tan)在直角三角形 …

All the trigonometric identities are based on the six trigonometric ratios. They are sine, cosine, tangent, cosecant, secant, and cotangent. All these trigonometric ratios are defined using the sides of the right triangle, such as an adjacent side, opposite side, and hypotenuse side.

Cosecant is one of the main six trigonometric functions and is abbreviated as csc x or cosec x, where x is the angle. In a right-angled triangle, cosecant is equal to the ratio of the hypotenuse and perpendicular. Since it is the reciprocal of sine, we write it as csc x = 1 / sin x.

Similar to the secant, the cosecant is defined by the reciprocal identity cscx = 1 sinx. Notice that the function is undefined when the sine is 0, leading to a vertical asymptote in the graph at 0, π, etc. Since the sine is never more than 1 in absolute value, the cosecant, being the reciprocal, will never be less than 1 in absolute value.