a) Complete the table and plot y = sin x X -360 3150 -270 -2250 -180 -135 -90 45 0 -0.7 0.7 0 -0.7 -7 -0.7 45 90 1350 180 225 270 315 360 0 0.7 1 0.7 0 -0.7 -1 -0.7 0 -3609 180- 180 6 270 360- b) The greatest value of the sine wave is called the amplitude. Why is the amplitude equal to1? (Hint: sin x = 0/4) . ...... The amplitude is always a positive quantity. c) Because the shape of the sine curve forms a regular pattern. We say such curves are periodic. A complete cycle of the sine wave is called a period. This is the width of the repeating pattern that is measured on the horizontal axis. What is the size of the period? d) What will happen as the sine graph as the angle increases? e) Use the graph of y = sin x to find the sine of these angles. (i) sin 30 (ii) sin 180 (iii) sin 630 (iv) sin 3420 (v) sin 2520 (vi) sin 360 (vii) sin 1080 (vili) sin 3060 f) Use the graph of y = sin x to solve the following equations for angles between -360 and 360. (Hint: There can be more than one Solution) (i) sin x = 0.5 (ii) sin x = 0.7 (iii) sin x = -0.5 (iv) sin x = -0.33. Here is the function y = tan x a) Complete the table and plot y = tan x X -360 -342 -333 -315 -2970 -288 -270 -252 Y -2430 -2250 -2070 -198 -180 1620 -1530 135 -117 -90 -450 450 900 135 180 2250 270 3150 360 -3609 -210% 180 380 b) The tangent function has a completely different shape. At 90, 270%, etc, the function is officially undefined, because it could be positive infinity or negative infinity. On the graph we represent these as asymptotes (dotted lines). Why does this happen? (Hint: tan x = /,) c) What is the size of the period? d) Use the graph of y = tan x to find the sine of these angles. (i) tan 540 (ii) tan 360 (iii) tan 990 (iv) tan 3420 e) Use the graph of y = tan x to solve the following equations for angles between -360" and 360. (Hint: There can be more than one Solution) (i) tan x = 1 (ii) tan x = 2 (iii) tan x = -3 (iv) tan x = -42. Here is the function y = cos x ) Complete the table and plot y = cos x X -360 -3150 -270 2750 -180 -135 -900 -45 450 900 1350 180 2250 270 315 360 -3609 -90 1803 270 b) Why is the amplitude equal to1? (Hint: cos x = 4/4) because the adjecent cannot be bigger than the hypotenuse as the hypotenuse is the largest side. c) What is the size of the period? d) The sine and cosine graphs are almost identical. What is the difference between them? e) We can the cosine curve is a sine curve which is shifted to the left. We call this a phase shift. How far left has it shifted? f) Use the graph of y = cos x to find the sine of these angles. (i) cos 600 (ii) cos 360 (ii) cos 990 (iv) cos 3420 g) Use the graph of y = cos x to solve the following equations for angles between -360 and 360. (Hint: There can be more than one Solution) (i) cos x = 0.5 (ii) cos x = 0.7 (iii) cos x = -0.5 (iv) cos x = -0.3