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The half-angle formula for cosine can be obtained by replacing with / and taking the square-root of both sides: (/) = (+ ) /. Sine power-reduction formula: an illustrative diagram. The shaded blue and green triangles, and the red-outlined triangle E B D {\displaystyle EBD} are all right-angled and similar, and all contain the angle θ ...
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.
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Write the functions without "co" on the three left outer vertices (from top to bottom: sine, tangent, secant) Write the co-functions on the corresponding three right outer vertices (cosine, cotangent, cosecant) Starting at any vertex of the resulting hexagon: The starting vertex equals one over the opposite vertex.
Fig. 1 – A triangle. The angles α (or A), β (or B), and γ (or C) are respectively opposite the sides a, b, and c.. In trigonometry, the law of cosines (also known as the cosine formula or cosine rule) relates the lengths of the sides of a triangle to the cosine of one of its angles.
The six trigonometric functions are defined for every real number, except, for some of them, for angles that differ from 0 by a multiple of the right angle (90°). Referring to the diagram at the right, the six trigonometric functions of θ are, for angles smaller than the right angle:
List of trigonometric identities#Power-reduction formulae To a section : This is a redirect from a topic that does not have its own page to a section of a page on the subject. For redirects to embedded anchors on a page, use {{ R to anchor }} instead .
In mathematics, the values of the trigonometric functions can be expressed approximately, as in (/), or exactly, as in (/) = /.While trigonometric tables contain many approximate values, the exact values for certain angles can be expressed by a combination of arithmetic operations and square roots.