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Become a Trigonometry & Precalculus Master by Udemy
Learn everything from Trigonometry and Precalculus, then test your knowledge with 470+ practice questions
Course Highlights
- Angles and their measure, including degrees, DMS and radians
- Six circular functions, including sine, cosine, tangent, cosecant, secant, and cotangent
- The unit circle, including finding sine and cosine, and how to complete a triangle
- Angles in circles, including oriented arcs, circular sectors, and linear and angular velocity
- Graphing the trig functions, including sine and cosine graphs, and transformations
- Inverse trig functions, including their graphs
- Trig identities, including even-odd, sum-difference, half-angle, double-angle, product-to-sum, and sum-to-product identities
- The law of sines and the law of cosines, including Heron's formula
- Polar curves, including converting coordinates and graphing polar curves
- Complex numbers, including polar forms and De Moivre's theorem
- Matrices, including solving systems, Gauss-Jordan elimination, and transformations and inverses
- Partial fractions, including fraction decomposition for all factor types
- Conic sections and analytic geometry, including rotating conics and polar equations of conics
- Parametric curves, including finding the direction of the parameter and the parametric representation
Skills you will learn!
Curriculum
4 Topics
What we'll learn in Trigonometry
How to get the most out of this course
Download the Trigonometry formula sheet
The EVERYTHING download
21 Topics
Introduction to angles
RESOURCE: Quiz solutions for this section
Naming angles
Naming angles
Naming angles
Complementary and supplementary angles
Complementary and supplementary angles
Complementary and supplementary angles
Positive and negative angles
Positive and negative angles
Positive and negative angles
Quadrant of the angle
Quadrant of the angle
Quadrant of the angle
Degrees radians and DMS
Degrees radians and DMS
Degrees radians and DMS
Coterminal angles
Coterminal angles
Coterminal angles
BONUS! Extra practice problems. :)
21 Topics
Introduction to the six trig functions
RESOURCE: Quiz solutions for this section
Sine cosine and tangent
Sine cosine and tangent
Sine cosine and tangent
Cosecant secant cotangent and the reciprocal identities
Cosecant secant cotangent and the reciprocal identities
Cosecant secant cotangent and the reciprocal identities
The quotient identities
The quotient identities
The quotient identities
The Pythagorean identities
The Pythagorean identities
The Pythagorean identities
Signs by quadrant
Signs by quadrant
Signs by quadrant
When the trig functions are undefined
When the trig functions are undefined
When the trig functions are undefined
BONUS! Extra practice problems. :)
33 Topics
Introduction to the unit circle
RESOURCE: Quiz solutions for this section
The unit circle
The unit circle
The unit circle
Negative angles and angles more than one rotation
Negative angles and angles more than one rotation
Negative angles and angles more than one rotation
Coterminal angles in a particular interval
Coterminal angles in a particular interval
Coterminal angles in a particular interval
Reference angles
Reference angles
Reference angles
Symmetry across axes
Symmetry across axes
Symmetry across axes
Even-odd identities
Even-odd identities
Even-odd identities
The set of all possible angles
The set of all possible angles
The set of all possible angles
Points not on the unit circle
Points not on the unit circle
Points not on the unit circle
Solving right triangles
Solving right triangles
Solving right triangles
Angles of elevation and depression
Angles of elevation and depression
Angles of elevation and depression
BONUS! Extra practice problems. :)
18 Topics
Introduction to angles in circles
RESOURCE: Quiz solutions for this section
Radians and arc length
Radians and arc length
Radians and arc length
Area of a circular sector
Area of a circular sector
Area of a circular sector
Trig functions of real numbers
Trig functions of real numbers
Trig functions of real numbers
Linear and angular velocity
Linear and angular velocity
Linear and angular velocity
Relating linear and angular velocity
Relating linear and angular velocity
Relating linear and angular velocity
BONUS! Extra practice problems. :)
24 Topics
Introduction to graphing trig functions
RESOURCE: Quiz solutions for this section
Sketching sine and cosine
Sketching sine and cosine
Sketching sine and cosine
Sketching cosecant and secant
Sketching cosecant and secant
Sketching cosecant and secant
Period and amplitude
Period and amplitude
Period and amplitude
Sketching tangent and cotangent
Sketching tangent and cotangent
Sketching tangent and cotangent
Horizontal and vertical shifts
Horizontal and vertical shifts
Horizontal and vertical shifts
Graphing transformations
Graphing transformations
Graphing transformations
Graphing combinations
Graphing combinations
Graphing combinations
BONUS! Extra practice problems. :)
12 Topics
Introduction to inverse trig functions
RESOURCE: Quiz solutions for this section
Inverse trig relations
Inverse trig relations
Inverse trig relations
Inverse trig functions
Inverse trig functions
Inverse trig functions
Trig functions of inverse trig functions
Trig functions of inverse trig functions
Trig functions of inverse trig functions
BONUS! Extra practice problems. :)
30 Topics
Introduction to trig identities
RESOURCE: Quiz solutions for this section
Sum-difference identities for sine and cosine
Sum-difference identities for sine and cosine
Sum-difference identities for sine and cosine
Cofunction identities
Cofunction identities
Cofunction identities
Sum-difference identities for tangent
Sum-difference identities for tangent
Sum-difference identities for tangent
Double-angle identities
Double-angle identities
Double-angle identities
Half-angle identities
Half-angle identities
Half-angle identities
Product-to-sum identities
Product-to-sum identities
Product-to-sum identities
Sum-to-product identities
Sum-to-product identities
Sum-to-product identities
Proving the trig equation
Proving the trig equation
Proving the trig equation
Complete solution set of the equation
Complete solution set of the equation
Complete solution set of the equation
BONUS! Extra practice problems. :)
18 Topics
Introduction to the law of sines and law of cosines
RESOURCE: Quiz solutions for this section
Law of sines
Law of sines
Law of sines
The ambiguous case of the law of sines
The ambiguous case of the law of sines
The ambiguous case of the law of sines
Area from the law of sines
Area from the law of sines
Area from the law of sines
Law of cosines
Law of cosines
Law of cosines
Heron's formula
Heron's formula
Heron's formula
BONUS! Extra practice problems. :)
3 Topics
Practice final exam #1 (optional)
Practice final exam #2 (optional)
Trigonometry final exam
2 Topics
What we'll learn in Precalculus
Download the Precalculus formula sheet
33 Topics
Introduction to polar curves
RESOURCE: Quiz solutions for this section
Polar coordinates
Polar coordinates
Polar coordinates
Multiple ways to express polar points
Multiple ways to express polar points
Multiple ways to express polar points
Converting equations
Converting equations
Converting equations
Graphing polar curves in a rectangular system
Graphing polar curves in a rectangular system
Graphing polar curves in a rectangular system
Graphing circles
Graphing circles
Graphing circles
Graphing roses
Graphing roses
Graphing roses
Graphing cardioids
Graphing cardioids
Graphing cardioids
Graphing limaçons
Graphing limaçons
Graphing limaçons
Graphing lemniscates
Graphing lemniscates
Graphing lemniscates
Intersection of polar curves
Intersection of polar curves
Intersection of polar curves
BONUS! Extra practice problems. :)
30 Topics
Introduction to complex numbers
RESOURCE: Quiz solutions for this section
Complex numbers
Complex numbers
Complex numbers
Complex number operations
Complex number operations
Complex number operations
Graphing complex numbers
Graphing complex numbers
Graphing complex numbers
Distances and midpoints
Distances and midpoints
Distances and midpoints
Complex numbers in polar form
Complex numbers in polar form
Complex numbers in polar form
Multiplying and dividing polar forms
Multiplying and dividing polar forms
Multiplying and dividing polar forms
Powers of complex numbers and De Moivre's Theorem
Powers of complex numbers and De Moivre's Theorem
Powers of complex numbers and De Moivre's Theorem
Complex number equations
Complex number equations
Complex number equations
Roots of complex numbers
Roots of complex numbers
Roots of complex numbers
BONUS! Extra practice problems. :)
39 Topics
Introduction to matrices
RESOURCE: Quiz solutions for this section
Matrix dimensions and entries
Matrix dimensions and entries
Matrix dimensions and entries
Representing systems with matrices
Representing systems with matrices
Representing systems with matrices
Simple row operations
Simple row operations
Simple row operations
Gauss-Jordan elimination and reduced row-echelon form
Gauss-Jordan elimination and reduced row-echelon form
Gauss-Jordan elimination and reduced row-echelon form
Matrix addition and subtraction
Matrix addition and subtraction
Matrix addition and subtraction
Scalar multiplication and zero matrices
Scalar multiplication and zero matrices
Scalar multiplication and zero matrices
Matrix multiplication
Matrix multiplication
Matrix multiplication
Identity matrices
Identity matrices
Identity matrices
Transformations
Transformations
Transformations
Matrix inverses and invertible and singular matrices
Matrix inverses and invertible and singular matrices
Matrix inverses and invertible and singular matrices
Solving systems with inverse matrices
Solving systems with inverse matrices
Solving systems with inverse matrices
Solving systems with Cramer's Rule
Solving systems with Cramer's Rule
Solving systems with Cramer's Rule
BONUS! Extra practice problems. :)
21 Topics
Introduction to partial fractions
RESOURCE: Quiz solutions for this section
Fraction decomposition
Fraction decomposition
Fraction decomposition
Distinct linear factors
Distinct linear factors
Distinct linear factors
Repeated linear factors
Repeated linear factors
Repeated linear factors
Distinct quadratic factors
Distinct quadratic factors
Distinct quadratic factors
Repeated quadratic factors
Repeated quadratic factors
Repeated quadratic factors
Mixed factors
Mixed factors
Mixed factors
BONUS! Extra practice problems. :)
24 Topics
Introduction to conic sections and analytic geometry
RESOURCE: Quiz solutions for this section
Identifying conic sections
Identifying conic sections
Identifying conic sections
Circles
Circles
Circles
Ellipses
Ellipses
Ellipses
Parabolas
Parabolas
Parabolas
Hyperbolas
Hyperbolas
Hyperbolas
Rotating axes
Rotating axes
Rotating axes
Polar equations of conics
Polar equations of conics
Polar equations of conics
BONUS! Extra practice problems. :)
12 Topics
Introduction to parametric curves
RESOURCE: Quiz solutions for this section
Parametric curves and eliminating the parameter
Parametric curves and eliminating the parameter
Parametric curves and eliminating the parameter
Direction of the parameter
Direction of the parameter
Direction of the parameter
Finding the parametric representation
Finding the parametric representation
Finding the parametric representation
BONUS! Extra practice problems. :)
4 Topics
Practice final exam #1 (optional)
Practice final exam #2 (optional)
Precalculus final exam
Wrap-up
Become a Trigonometry & Precalculus Master
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