The cyclic nature of the sine and cosine graphs is incredibly important throughout science, nature and engineering. When working with a unit circle we can measure cos, sin and tan directly: The 'Unit Circle' is a special case of the circle shown in the diagrams above. Sin θ is therefore positive and Cos θ is negative. The value of θ is between 270° and 360°, the green line is positive, but the red and blue lines are negative. Sines and cosines are therefore all positive in value.ĭiagram iv shows the final quadrant. The green, red and blue lines all have negative values and α = θ − 180°. In Diagram iii, the radius has rotated further anticlockwise into the next quadrant so that the value of θ is between 180° and 270°. Cos θ = −Cos α =Ĭos θ is negative, since the green line is negative (it lies along the x axis to the left of the origin (0,0), so is in the negative section of the x axis). Sin θ = Sin α =īoth the blue and red lines are positive, so sin θ is positive. The reference angle alpha α is equal to 180° − θ, and is the acute angle within the right-angled triangle. Here θ is an obtuse angle, between 90° and 180°. In Diagram ii, we have rotated the radius further in an anti-clockwise direction, past the vertical (y axis) into the next quadrant. We then rotate the radius in an anticlockwise direction through an angle theta θ. Understanding Statistical Distributionsĭiagram i shows what happens if we draw a radius from the centre of the circle to the right along the x axis (we say this is in a positive direction).Area, Surface Area and Volume Reference Sheet.
Simple Transformations of 2-Dimensional Shapes.Polar, Cylindrical and Spherical Coordinates.Introduction to Cartesian Coordinate Systems.Introduction to Geometry: Points, Lines and Planes.Percentage Change | Increase and Decrease.
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