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Trigonometry Angles--Pi/4

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TrigonometryAnglesPi4Diagram

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 sintheta=costheta immediately gives

sin(1/4pi)=cos(1/4pi)=1/2sqrt(2).
(2)
TrigonometryAnglesPi4

Filling in the rest of the trigonometric functions then gives

cos(pi/4)=1/2sqrt(2)
(3)
cot(pi/4)=1
(4)
csc(pi/4)=sqrt(2)
(5)
sec(pi/4)=sqrt(2)
(6)
sin(pi/4)=1/2sqrt(2)
(7)
tan(pi/4)=1.
(8)

See also

Square, Trigonometry Angles, Trigonometry, Trigonometry Angles--Pi/2, Trigonometry Angles--Pi/8, Trigonometry Angles--Pi/16

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Cite this as:

Weisstein, Eric W. "Trigonometry Angles--Pi/4." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/TrigonometryAnglesPi4.html

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