1. Sine, Cosine and Tangent Angles Objectives (a) Explain what is meant by quadrant (b) Sketch sine, cosine and tangent curves

2. What is a quadrant The sine quadrant (Arabic: Rubul mujayyab, الربع المجيب ) was a type of quadrant used by medieval Arabic astronomers. It is also known as a "sinecal quadrant" in the English-speaking world. The instrument could be used to measure celestial angles, to tell time, to find directions, or to determine the apparent positions of any celestial object for any time. Is defined as one quarter of a circle

4. Quadrants I = 1 st quadrant II = 2 nd quadrant III = 3 rd quadrant IV = 4 th quadrant

5. The first quadrant contains all the points with positive x and positive y coordinates and is represented by the roman numeral I. The second quadrant contains all the points with negative x and positive y coordinates and is represented by the roman numeral II. The third quadrant contains all the points with negative x and negative y coordinates and is represented by the roman numeral III. The fourth quadrant contains all the points with positive x and negative y coordinates and is represented by the roman numeral IV +X-X +Y -Y

6. Sine Curve 1. The sine graph starts at zero 2. It repeats itself every 360 degrees 3. y is never more than 1 or less than -1 4. A sin graph 'leads' a cosine graph by 90 degrees http://www.math.utah.edu/~palais/cossin.html

7. Cosine curve 1. The cosine graph starts at one 2. It repeats itself every 360 degrees 3. y is never more than 1 or less than -1 4. A cosine graph 'lags' a sine graph by 90 degrees

8. Compare Sine and cosine curves Red curve = sine wave Green curve = cosine wave

9. Tangent curve 1. The tangent graph starts at zero 2. It repeats itself every 180 degrees 3. y can vary between numbers approaching infinity and minus infinity

10. Plot the curves Using the issued task sheet carry out the following (a) For the trigonometric functions complete the table for sine, cosine and tan form zero degrees to 360 degrees. (b) Separately plot the three trigonometric functions over one complete cycle (c) Put you name and date on each piece of evidence

11. Use the table provided to complete each of the trigonometric functions through one complete cycle. Ensure all axes are labelled clearly and correctly on the graph Ensure graph and each line has a title.