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Sine function on unit circle (top) and its graph (bottom) In this illustration, the six trigonometric functions of an arbitrary angle θ are represented as Cartesian coordinates of points related to the unit circle. The y-axis ordinates of A, B and D are sin θ, tan θ and csc θ, respectively, while the x-axis abscissas of A, C and E are cos ...
Similar right triangles illustrating the tangent and secant trigonometric functions Trigonometric functions and their reciprocals on the unit circle. The Pythagorean theorem applied to the blue triangle shows the identity 1 + cot 2 θ = csc 2 θ, and applied to the red triangle shows that 1 + tan 2 θ = sec 2 θ.
Masing-masing ordinat A, B dan D merupakan nilai dari sin θ, tan θ dan csc θ, sedangkan masing-masing absis dari A, C dan E merupakan nilai cos θ, cot θ dan sec θ. العربية: في هذا الرسم، الدوال المثلثية الستة لزاوية اختيارية θ ممثلة إحداثياتٍ ديكارتية للنقاط ...
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Trigonometric functions and their reciprocals on the unit circle. All of the right-angled triangles are similar, i.e. the ratios between their corresponding sides are the same. For sin, cos and tan the unit-length radius forms the hypotenuse of the triangle that defines them.
English: A unit circle with sine (sin), cosine (cos), tangent (tan), cotangent (cot), versine (versin), coversine (cvs), exsecant (exsec), excosecant (excsc) and (indirectly) also secant (sec), cosecant (csc) as well as chord (crd) and arc labeled as trigonometric functions of angle theta. It is designed as alternative construction to "Circle ...
Since C = 2πr, the circumference of a unit circle is 2π. In mathematics, a unit circle is a circle of unit radius—that is, a radius of 1. [1] Frequently, especially in trigonometry, the unit circle is the circle of radius 1 centered at the origin (0, 0) in the Cartesian coordinate system in the Euclidean plane.
The sign of the square root needs to be chosen properly—note that if 2 π is added to θ, the quantities inside the square roots are unchanged, but the left-hand-sides of the equations change sign. Therefore, the correct sign to use depends on the value of θ. For the tan function, the equation is: