Survey
* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
Trigonometry rules review Use Soh Cah Toa (o) Opposite Sin θ x cm (a) Adjacent (h) Hypotenuse Cos θ (h) Hypotenuse 1 cm 90° 20° (o) Opposite Tan θ (opposite side) (a) Adjacent Hypotenuse (longest side) h o θ (adjacent side) Sin θ = the ratio 180° 0° a of the opposite side the hypotenuse 270° Calculators in DEGREES Generating the sin graph by rotating around a circle 90° 180° x 0 30 60 90 120 150 180 210 Sinx 0° 270° Trig Graphs: Introduction The functions based on y = Sin(x), y = Cos(x), and y = Tan(x) produce trig graphs. The Sin & Cos graphs are periodic, described by the amplitude & period Periodic: repeated cycle of values sideways translation maps the graph back onto itself Period (Wavelength) Period: time taken for 1 cycle to pass Length of 1 cycle = wavelength Amplitude Amplitude: half the ‘max y’ – ‘min y’ values (from the middle to top) Basic Sin & Cos graphs have amplitude = 1 yy = Sin x 1 Theta Ex34.01 1 90 180 270 360 x -360 -270 -180 -90 -1 y = Cos x y 90 -1 180 270 360 x y y y 1 2 1 0.5 1.5 1 0.5 0.5 90 180 – 0.5 270 360 x 90 180 270 – 0.5 – 0.5 – 1 360 x 90 180 270 – 1 – 1 – 1.5 – 2 y = Sin(x) Features Amplitude Period Symmetry Theta Ex34.01 y = Cos(x) Features – 2.5 HW p153 y = Tan(x) Features 360 x Exploring the features of the graphs y 1 1) Any angle with a negative ‘Cos’ value must be between…… 90 180 270 360 x -1 2) If Cos(60°) = 0.5 what other angle is possible for Cos(x°) = 0.5 (between 0 and 360°) .5 .5 3) If Cos (x) = -0.4, what two angles (between 0 and 360°) are possible y 2 For 0 < x < 90° Sin(x) Cos(x) Tan(x) For 90° < x < 180° Sin(x) Cos(x) Tan(x) 1.5 1 0.5 – 0.5 – 1 90 180 270 360 x For 180° < x < 270° Sin(x) Cos(x) Tan(x) For 270° < x < 360° Cos(x) Tan(x) – 1.5 – 2 – 2.5 Sin(x)