Trigonometry Angles--Pi/4
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
[画像:cos(pi/4)] = 1/2sqrt(2)
(3)
[画像:cot(pi/4)] = 1
(4)
[画像:csc(pi/4)] = sqrt(2)
(5)
[画像:sec(pi/4)] = sqrt(2)
(6)
[画像:sin(pi/4)] = 1/2sqrt(2)
(7)
[画像:tan(pi/4)] = 1.
(8)
See also
Square, Trigonometry Angles, Trigonometry, Trigonometry Angles--Pi/2, Trigonometry Angles--Pi/8, Trigonometry Angles--Pi/16Explore with Wolfram|Alpha
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Cite this as:
Weisstein, Eric W. "Trigonometry Angles--Pi/4." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/TrigonometryAnglesPi4.html