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Unit circle definition of sin, cos, tan using radians

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Let $A$ be the point $(1,0)$, $O$ be the origin $(0,0)$, and $B$ be a point on the unit circle (the circle centred at the origin, $O$, with radius 1). 

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Suppose that the line segment $OA$ would have to travel $\\theta$ radians anti-clockwise around the origin to get to the line segment $OB$. In other words, $B$ is $\\theta$ radians anti-clockwise from the positive $x$-axis.

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The point on the unit circle, $\\theta$ radians anti-clockwise from the positive $x$-axis, is $(\\cos(\\theta),\\sin(\\theta))$. This is the unit circle definition of sine and cosine. You can think of this as being a generalisation of the right-angled trigonometry that takes place in the first quadrant of the Cartesian plane.

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The definition of $\\tan(\\theta)$ can be thought of as $\\dfrac{\\sin(\\theta)}{\\cos(\\theta)}$ but this is just the gradient of the line segment connecting the origin to the point on the unit circle.

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The following applet is for you to investigate the relationship between the trigonometric functions and the unit circle by moving the point $B$ around the circle.

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What are the coordinates of the point $B$ (the point on the unit circle $\\theta$ radians anticlockwise from the positive $x$-axis)?

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$B=\\Large($ [[0]], [[1]] $\\Large)$

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Note: Suppose you wanted to enter $\\tan(\\theta)$, then you would type tan(theta) including the brackets.

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What is the slope of the line segment $OB$?

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$m_{OB}=$ [[0]]

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