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Given two intersecting lines, the two nonadjacent angles with the same vertex are said to be vertical angles. One can easily prove that vertical angles are congruent. Some ...
Two angles alpha and beta are said to be complementary if alpha+beta=pi/2. In other words, alpha and beta are complementary angles if they produce a right angle when combined.
Two angles alpha and beta for which alpha+beta=pi are said to be supplementary. In other words, alpha and beta are supplementary angles if they produce a straight angle when ...
The angles S_1=A_1/2 and S_2=A_2/2 obtained from solving sin(x+omega)=2sinomega (1) for x=A_1,A_2, where omega is the Brocard angle. The half-angles A_1 and A_2 are given by ...
According to Euler's rotation theorem, any rotation may be described using three angles. If the rotations are written in terms of rotation matrices D, C, and B, then a ...
The angles mpi/n (with m,n integers) for which the trigonometric functions may be expressed in terms of finite root extraction of real numbers are limited to values of m ...
cos(pi/(12)) = 1/4(sqrt(6)+sqrt(2)) (1) cos((5pi)/(12)) = 1/4(sqrt(6)-sqrt(2)) (2) cot(pi/(12)) = 2+sqrt(3) (3) cot((5pi)/(12)) = 2-sqrt(3) (4) csc(pi/(12)) = sqrt(6)+sqrt(2) ...
Construction of the angle pi/4=45 degrees produces an isosceles right triangle. Since the sides are equal, sin^2theta+cos^2theta=2sin^2theta=1, (1) so solving for ...
cos(pi/(15)) = 1/8(sqrt(30+6sqrt(5))+sqrt(5)-1) (1) cos((2pi)/(15)) = 1/8(sqrt(30-6sqrt(5))+sqrt(5)+1) (2) cos((4pi)/(15)) = 1/8(sqrt(30+6sqrt(5))-sqrt(5)+1) (3) ...
Construction of the angle pi/3=60 degrees produces a 30-60-90 triangle, which has angles theta=pi/3 and theta/2=pi/6. From the above diagram, write y=sintheta for the ...
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