Sine Function: sin (θ) = Opposite / Hypotenuse. Cosine Function: cos (θ) = Adjacent / Hypotenuse. Tangent Function: tan (θ) = Opposite / Adjacent. When we divide Sine by Cosine we get: So we can say: That is our first Trigonometric Identity. We can also divide "the other way around" (such as Adjacent/Opposite instead of Opposite/Adjacent) to get:

Sin(θ), Tan(θ), and 1 are the heights to the line starting from the x-axis, while Cos(θ), 1, and Cot(θ) are lengths along the x-axis starting from the origin. If the acute angle θ is given, then any right triangles that have an angle of θ are similar to each other.

Trigonometry Functions - Sin, Cos, Tan, Csc, Sec and Cot. Tangent, cotangent, secant, and cosecant of any angle. This tutorial covers the reciprocal identities and shows them in various forms.

The properties of the 6 trigonometric functions: sin (x), cos (x), tan(x), cot (x), sec (x) and csc (x) are discussed. These include the graph, domain, range, asymptotes (if any), symmetry, x and y intercepts and maximum and minimum points.

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 .

Mar 7, 2025 · They are based on the six fundamental trigonometric functions: sine (sin), cosine (cos), tangent (tan), cosecant (cosec), secant (sec), and cotangent (cot). All the identities are derived from the six trigonometric functions and are used to simplify expressions, verify equations, and solve trigonometric problems.

Feb 24, 2025 · The smallest periodic cycle for sine, cosine, secant, and cosecant is 2π, while for tangent and cotangent, it is π. The periodic properties of the trigonometric functions are given below: sin(x + 2nπ) = sin x; cos(x + 2nπ) = cos x; tan(x + nπ) = tan x; cot(x + nπ) = cot x; cosec(x + 2nπ) = cosec x; sec(x + 2nπ) = sec x; Here, n is any ...