Trigonometry: Sine, Cosine, Tangent

[general angle][ sine ][ cosine ][ tangent ]





The General Angle

Consider a radius of length '1' rotating anti-clockwise about the origin. The coordinates of any point on the circle give the values of the adjacent and opposite sides of a right angled triangle, with the radius the hypotenuse.

The General Angle (theta) is the included angle between the radius and the x-coordinate of the point.

As the radius rotates the x and y values change. Hence the values of sine, cosine and tangent also change.

sin cos tan ratios


sin cos tan compared

The result is summarized in the diagram below.

all sin tan cos when positive

Example #1

sin cos tan problem#1

sin cos tan problem#1

sin cos tan problem#1 continued

Example #2

general angle problem#2

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sine curve


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cosine curve


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tangent curve

Further comparison




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