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Master Leaving Cert Trigonometry

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Master trigonometric functions, identities, and applications

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Trigonometry Topics

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Right Triangle Trigonometry
Use sine ratio to calculate angles and sides (Sin = oh \frac{o}{h}ho​ )
Use cosine ratio to calculate angles and sides (Cos = ah \frac{a}{h}ha​ )
Use tangent ratio to calculate angles and sides (Tan = oa \frac{o}{a}ao​ )
Combination of SohCahToa questions
Solving expressions using 45-45-90 special right triangles
Solving expressions using 30-60-90 special right triangles
Word problems relating ladder in trigonometry
Word problems relating guy wire in trigonometry
Other word problems relating angles in trigonometry
video
Trigonometric Ratios and Angle Measure
Angle in standard position
Coterminal angles
Reference angle
Find the exact value of trigonometric ratios
ASTC rule in trigonometry (All Students Take Calculus)
Unit circle
Converting between degrees and radians
Trigonometric ratios of angles in radians
Radian measure and arc length
Law of sines
Law of cosines
Applications of the sine law and cosine law
video
Bearings
Introduction to bearings
Bearings and direction word problems
Angle of elevation and depression
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Graphing Trigonometric Functions
Sine graph: y = sin x
Cosine graph: y = cos x
Tangent graph: y = tan x
Cotangent graph: y = cot x
Secant graph: y = sec x
Cosecant graph: y = csc x
Graphing transformations of trigonometric functions
Determining trigonometric functions given their graphs
video
Applications of Trigonometric Functions
Ferris wheel trig problems
Tides and water depth trig problems
Spring (simple harmonic motion) trig problems
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Trigonometric Identities
Quotient identities and reciprocal identities
Pythagorean identities
Sum and difference identities
Cofunction identities
Double-angle identities
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Solving Trigonometric Equations
Solving first degree trigonometric equations
Determining non-permissible values for trig expressions
Solving second degree trigonometric equations
Solving trigonometric equations involving multiple angles
Solving trigonometric equations using pythagorean identities
Solving trigonometric equations using sum and difference identities
Solving trigonometric equations using double-angle identities
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Inverse Trigonometric Functions
Finding inverse trigonometric function from its graph
Evaluating inverse trigonometric functions
Finding inverse reciprocal trigonometric function from its graph
Finding exact value of inverse reciprocal trig functions
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Imaginary and Complex Numbers
Introduction to imaginary numbers
Complex numbers and complex planes
Adding and subtracting complex numbers
Complex conjugates
Multiplying and dividing complex numbers
Distance and midpoint of complex numbers
Angle and absolute value of complex numbers
Polar form of complex numbers
Operations on complex numbers in polar form

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