Graphs of SINE & COSINE of Angles SS1 Mathematics Lesson Note

GRAPH OF SINE AND COSINE OF ANGLES

Draw a circle on a Cartesian plane so that its radius, OP, is of length 1 unit. Such a circle is called a unit circle.

The angle Ѳ that OP makes with Ox changes according to the position of P on the circumference of the unit circle. Since P is the point (x,y) and /OP/ = 1 unit,

         Sin Ѳ = y/1     = y

          Cos Ѳ = x/1   = x

Hence the values of x and y give a measure of cos Ѳ and sin Ѳ respectively.

If the values of Ѳ are taken from the unit circle, they can be used to draw the graph of sin Ѳ. This is done by plotting values of y against corresponding values of Ѳ.

To draw the graph of cosѲ, use corresponding values of x and Ѳ. This gives another wave-shaped curve,

Take note of the following:

1)All values of sin Ѳ and cos Ѳ lie between +1 and -1.

2)The sine and cosine curves have the same shapes but different starting points.

3)Each curve is symmetrical about its peak(high point) and trough(low point). This means that for any value of sin Ѳ there are usually two angles between 0 o and 360 o; likewise for cos Ѳ. The only exceptions to this are at the quarter turns, where sinѲ and cosѲ have the values given in the table below:

ASSIGNMENT 

1. If Sin A  = 4/5, what is tan A? A 2/5 B. 3/5 C. ¾    D. 1 E. 4/3
2. Use tables to find the value of 8 Cos 77. A. 5.44    B. 6.48     C. 9.12 D 7.57 E. 1.80
3. If cos θ = sin 33 o, find tan θ. A.1.540 B. 2.64 C.0.64 D. 1.16 E. 1.32
4. If the diagonal of a square is 8cm, what is the area of the square? A.16cm2B. 2cm2 C. 4cm2D. 20cm2E. 10cm2
5. Calculate the angle which the diagonal in question 4 makes with any of the sides of the square .A. 65oB. 45oC. 35oD. 25oE. 75o

6. From a place 400m north of X, a student walks eastwards to a place Y which is 800m from X. What is the bearing of X from Y?

7. In the figure below, the right angles and lengths of sides are as shown. Calculate the value of K.