Relationship between Sine and Tangent
Relationship between Sine and Tangent
This Demonstration shows the relation between , the measure of the angle, and , where .
sin(x)
x
tan(x)
0⩽x<
π
2
You can choose the measure of the angle using the slider or by dragging the hypotenuse.
x
The length of the blue line is the sine of the angle (defined by the length of the green arc); the length of the orange line is the tangent of the same angle.
The blue line is always shorter than the green arc; therefore .
sin(x)≤x
Check the "compare…" button to compare the area of the yellow triangular region and that of the dark circular sector. The area of the triangle is equal to 1tan(x); the area of the circular sector is equal to 1x.
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2
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2