manual derivatives done using the definition 54 videos

The Definitions of Sine and Cosine
Precalculus Trigonometric Functions
How we define sine and cosine for all angle measures using the unit circle.
sine cosine right triangle definitions of sine and cosine angles in standard position unit circle definitions of sine and cosine 
Using the Complement to Calculate Probability
Precalculus Topics in Discrete Math
How to use the complement to calculate the probability of an event.
complement probability odds chances 
Using Trigonometric Identities
Precalculus Trigonometric Functions
How to simplify a trigonometric expression by converting to sines and cosines and using algebra.
reciprocal identities 
Using Sine to Calculate the Area of a Triangle
Precalculus Basic Trigonometry
How to calculate the area of any triangle using two sides and an included angle.
area of a triangle sine 
The Circle
Precalculus Conic Sections
How to use the distance formula to derive the equation for a circle.
circle center radius distance formula equation for a circle 
The Circle
Precalculus Equations of Lines, Parabolas and Circles
How to use the distance formula to derive the equation for a circle.
circle center radius distance formula equation for a circle 
Using the Sine and Cosine Addition Formulas to Prove Identities
Precalculus Advanced Trigonometry
How to use the sine and cosine addition formulas to prove the cofunction identities.
the cosine addition formulas the sine addition formulas 
Using the Conjugate Zeros Theorem
Precalculus Polynomial and Rational Functions
How we find the zeros of a polynomial function when one imaginary zero is known.
polynomial functions quadratic functions zeros multiplicity the conjugate zeros theorem the conjugate roots theorem conjugates imaginary numbers imaginary zeros 
Using the Inverse Trigonometric Functions
Precalculus Advanced Trigonometry
How to evaluate expressions like tan(sin (4/5))^(1).
sine cosine tangent inverse sine inverse cosine inverse tangent the unit circle 
Trigonometric Identities
Precalculus Trigonometric Functions
How to use the unit circle to derive the tangent identity and the Pythagorean identity.
identities the unit circle trigonometric identities the Pythagorean identity 
The HalfAngle Identities
Precalculus Advanced Trigonometry
How to use the power reduction formulas to derive the halfangle formulas.
the power reduction formulas the half angle formulas quadrants 
The Cosine Addition Formulas
Precalculus Advanced Trigonometry
How to derive the cosine of a difference formula.
the unit circle the law of cosines the distance formula cosine of a difference formula 
The Sine Addition Formulas
Precalculus Advanced Trigonometry
How to derive the sine of a sum formula.
cosine of a difference formula the cofunction identities the sine of a sum formula 
Graphing the Reciprocal Trigonometric Functions
Precalculus Trigonometric Functions
How to use the unit circle to derive identities that are useful in graphing the reciprocal trigonometric functions.
identities the unit circle the cofunction identities the "add Π@" identities 
The Midpoint and Distance Formulas in 3D
Precalculus Vectors and Parametric Equations
How to derive the formula for the midpoint of a segment in three dimensions.
position vectors the vector from point a to point b the midpoint formula vector addition scalar multiplication 
The Distance Formula in Polar Coordinates
Precalculus Polar Coordinates and Complex Numbers
How to derive the distance formula for polar coordinates.
polar coordinates the law of cosines triangles 
Solving Linear Systems Using Matrix Algebra
Precalculus Systems of Linear Equations and Matrices
How to convert a system of linear equations into a matrix equation and solve it.
matrices square matrices matrix equation coefficient matrix inverse matrix identity matrix matrix multiplication 
Logarithmic Functions
Precalculus Exponential and Logarithmic Functions
How to graph logarithmic functions.
logarithmic functions exponential functions graphs of logarithmic functions definition of a logarithm 
Evaluating Sine and Cosine at Special Acute Angles
Precalculus Trigonometric Functions
How do we measure sine and cosine of pi/4?
sine cosine unit circle definitions of sine and cosine angles in standard position