Trig CAST Diagram-Grade 12 Reduction Rules, Special Angles and Compound Angles PART 2
24 minute lessons
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Trig CAST Diagram-Grade 12 Reduction Rules, Special Angles and Compound Angles PART 2
776 просмотров · 3 г. назад
24 minute lessons
88,4 тыс. подписчиков
776 просмотров · 3 г. назад
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Co-function Identities: These identities relate complementary angles. They are:
sin(x) = cos(90°-x)
cos(x) = sin(90°-x)
tan(x) = cot(90°-x)
cot(x) = tan(90°-x)
Even-Odd Identities: These identities relate the evenness and oddness of trigonometric functions. They are:
sin(-x) = -sin(x)
cos(-x) = cos(x)
tan(-x) = -tan(x)
These identities can be used to simplify expressions by replacing an expression with its negative equivalent, or by replacing an even function with its corresponding even function or an odd function with its corresponding odd function.
Sum and Difference Identities: These identities allow us to calculate the values of trigonometric functions for the sum or difference of two angles. They are:
sin(x ± y) = sin(x)cos(y) ± cos(x)sin(y)
cos(x ± y) = cos(x)cos(y) ∓ sin(x)sin(y)
Double Angle Identities: The double angle identities relate the values of trigonometric functions for an angle that is twice the original angle. They are:
sin(2x) = 2sin(x)cos(x)
cos(2x) = cos^2(x) - sin^2(x) = 2cos^2(x) - 1 = 1 - 2sin^2(x)
tan(2x) = (2tan(x))/(1 - tan^2(x))
These identities can be used to simplify expressions by replacing an expression with an equivalent expression involving twice the original angle.
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