manual derivatives done using the definition 27 videos

The Definitions of Sine and Cosine
Trigonometry 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 Trigonometric Identities
Trigonometry 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
Trigonometry Basic Trigonometry
How to calculate the area of any triangle using two sides and an included angle.
area of a triangle sine 
Equation of a Circle
Trigonometry Pythagorean Theorem
How to derive the equation for a circle using the distance formula.
distance formula radius center circle 
Using the Sine and Cosine Addition Formulas to Prove Identities
Trigonometry 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 Inverse Trigonometric Functions
Trigonometry Advanced Trigonometry
How to evaluate expressions like tan(sin (4/5))^(1).
sine cosine tangent inverse sine inverse cosine inverse tangent the unit circle 
Using the Pythagorean Theorem to find a Missing Hypotenuse
Trigonometry Pythagorean Theorem
How to calculate the hypotenuse in a right triangle given the lengths of the legs using the Pythagorean Theorem.
Pythagorean theorem leg hypotenuse right triangle 
Using the Pythagorean Theorem to find a Missing Leg
Trigonometry Pythagorean Theorem
How to use the Pythagorean Theorem to find a missing leg, given the length of the hypotenuse and a leg.
Pythagorean theorem leg hypotenuse right triangle 
Distance Formula
Trigonometry Pythagorean Theorem
How to derive the equation for the distance between two points using the Pythagorean Theorem.
distance coordinate plane ordered pair segment 
Trigonometric Identities
Trigonometry 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
Trigonometry 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
Trigonometry 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
Trigonometry 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
Trigonometry 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 
Evaluating Sine and Cosine at Special Acute Angles
Trigonometry 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 
Other Forms of the Cosine DoubleAngle Formula
Trigonometry Advanced Trigonometry
How to derive two more cosine doubleangle formulas.
the Pythagorean identity the cosine double angle formulas 
The Law of Cosines
Trigonometry Basic Trigonometry
How to define and use the law of cosines.
law of cosines ratios triangles 
Evaluating Sine and Cosine at Other Special Angles
Trigonometry Trigonometric Functions
How to measure the sine and cosine of 150.
sine cosine unit circle definitions of sine and cosine angles in standard position reference angles 
Radian Measure of Angles
Trigonometry Trigonometric Functions
How to measure angles using degrees or radians.
angle degree measure acute angle right angle obtuse angle radian measure 
Converse of the Pythagorean Theorem
Trigonometry Pythagorean Theorem
How to use the converse of the Pythagorean Theorem to determine if a triangle is a right triangle, how to use Pythagorean triples to memorize the lengths of certain right triangles.
right triangle leg hypotenuse converse Pythagorean triples