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Published byAudrey Blair Modified over 2 years ago

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Presents Mathematics Department

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Graphs of Sine, Cosine and Tangent The combined graphs Summary Solving trigonometric equations Menu

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Graphs

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What about tan 70°? tan 80°? tan 85°? Can you explain whats happening?

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Sin xº xº Graph of Sin x°

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Cos xº Graph of Cos x° xº

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Tan xº Graph of Tan x° xº This isnt drawn to scale- but it looks something like this!

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0 - 90° Sin x ° +ve Cos x ° +ve Tan x ° +ve Combined Graphs xº Sin xº Cos xº Tan xº

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Sin x ° +ve Cos x ° -ve Tan x ° -ve Combined Graphs xº Sin xº Cos xº Tan xº 90°-180°

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Sin x ° -ve Cos x ° -ve Tan x ° +ve Combined Graphs xº Sin xº Cos xº Tan xº 180°-270°

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Sin x ° -ve Cos x ° +ve Tan x ° -ve Combined Graphs xº Sin xº Cos xº Tan xº 270°-360°

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270° 180° 90° 0°0° Summary

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270° 180° 90° 0°0° Sin x ° +ve Cos x ° +ve Tan x ° +ve Sin x ° +ve Cos x ° -ve Tan x ° -ve Sin x ° -ve Cos x ° -ve Tan x ° +ve Sin x ° -ve Cos x ° +ve Tan x ° -ve SinTanCosAll Which are positive? Summary

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270° 180° 90° 0°0° Sin x ° +ve Cos x ° +ve Tan x ° +ve Sin x ° +ve Cos x ° -ve Tan x ° -ve Sin x ° -ve Cos x ° -ve Tan x ° +ve Sin x ° -ve Cos x ° +ve Tan x ° -ve Sinners TakeCare! All Which are positive? Summary

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Cos x° = 0.50 x360 Cos xº xº °300° Example 1 So x = 60°, 300°

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270° 180° 90° 0°0° Cos x° = 0.50x360 A T S C (Cos ¹ 0.5 = 60°) 300° x = 60°, 300° Example 2 60° Cos +ve

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270° 180° 90° 0°0° Sin x° = -0.50x360 A T S C 30° Sin -ve (Sin ¹ 0.5 = 30°) Sin -ve, 330°x = 210° 30° Example 3

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270° 180° 90° 0°0° 2Sin x° = 10x360 A T S C (Sin ¹ ½ = 30°) x = 30° Sin x° = ½,150° 30º Example 4 Sin +ve

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270° 180° 90° 0°0° 3 cos x° = -1 0x360 A T S C cos -ve (cos ¹ = 70.5°) cos -ve, 250.5°x = 109.5° 3 cos x°+1 = 0 cos x° = ° Example 5

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Mathematics Department

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