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TRIGONOMETRIC GRAPHS Higher Tier GRAPHS OF TROGONOMETRIC RATIOS The graphs of y = sin x, y = cos x and y = tan x are widely used in electrical engineering, electronics, sound engineering and all studies of waves. You need to sketch the graphs of these trigonometric functions. You need to identify important facts about each of these graphs and remember their symmetry. You need to use these graphs to solve simple trigonometric equations. Accurate Graphs (for 0° x 360°) triggraphs ©RSH 12 April 2010 Passes through the origin, 180°, 360° Maximum 1 when x = 90° and Minimum 1. The AMPLITUDE is 1 Repeats every 360° Graph can be continued both ways indefinitely. Maximum 1 when x = 0° and Minimum 1. The AMPLITUDE is 1 Repeats every 360° Graph can be continued both ways indefinitely. Page 1 of 3 TRIGONOMETRIC GRAPHS Higher Tier Passes through the origin, 180°, 360° Maximum when x = 90° Minimum The vertical lines at x = 90°, 180° etc are called ASYMPTOTES. Repeats every 180° Graph can be continued both ways indefinitely. Solving Equations Solve the equation sin x = 0.5 giving all values in the range 0° x 360° Solution Using a calculator, x sin1 0.5 To give x = 30°. Looking at the graph of y = sin x, sin x = 0.5 twice in this range. x = 30° is the first, the second is 180° 30° = 150°. Answer: x = 30° and 150° Note: The answers can be checked in a calculator triggraphs ©RSH 12 April 2010 Page 2 of 3 TRIGONOMETRIC GRAPHS Higher Tier Solve the equation cos x = 0.5 giving all values in the range 90° x 360° Solution Using a calculator, x cos1 0.5 To give x = 60°. Looking at the graph of y = cos x, cos x = 0.5 three times in this range. x = 60° is the first, the second is 60° and the third is 360° 60° = 300°. Answer: x = 60°, 60°, 300° Solve the equation tan x = 1 giving all values in the range 90° x 360° Solution Using a calculator, x tan1 0.5 To give x = 45°. Looking at the graph of y = tan x, tan x = 1 three times in this range. x = 45° is the first, the second is 180° 45° = 135° and the third is 360° 45° = 315°. Answer: x = 45°, 135°, 315° Solve the equation sin x = 0.3 giving all values in the range 0° x 360° Solution Using a calculator, x sin1(0.3) To give x = 17.5°. Answer: x = 197.5°, 342.5° triggraphs ©RSH 12 April 2010 Page 3 of 3