Unit Circle to Sine Wave

Also called

unit circle · sine wave · sine curve · cosine curve · graph of sin x · graph of cos x · trigonometric functions · radian measure · radians and degrees · negative angles · tangent function · tan x · period 2π · phase shift · sin²x + cos²x = 1 · इकाई वृत्त · त्रिकोणमितीय फलन · रेडियन

Topics

• On the unit circle the point at angle x is (cos x, sin x): its height is sin x and its sideways shadow is cos x.
• As the point goes round once, its height draws one full wave of y = sin x: the period is 2π.
• The cosine curve is the sine curve moved π/2 to the left: cos x = sin(x + π/2).
• One radian is the angle whose arc is as long as the radius; a full turn is 2π radians, so π radians = 180°.
• Unrolled, the rim is 2π radii long, which is why the sine wave crosses its axis at π and 2π.
• Angles measured clockwise are negative: sin(−x) = −sin x, while cos(−x) = cos x.
• tan x = sin x / cos x is the length cut off on the tangent at (1, 0); it grows without limit near x = π/2.
• The height and the shadow are the legs of a right triangle with hypotenuse 1, so sin²x + cos²x = 1.

About this model

A GLB file of about 787 KB, shown in Lably's 3D viewer and, on a phone, placed in your room with AR. Credit: Model, science and animation: Lably (built procedurally with three.js; no downloaded meshes). | CC BY 4.0. Original geometry and animation made for Lably.

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