Trig Functions with the Unit Circle

Using the unit circle to sketch the graph of the tangent function

Graphing the reciprocal trig functions cosecant, secant, and cotangent

Using the difference identities of sine and cosine to derive the cofunction identities

Using the sum identities of sine and cosine to derive the double angle identities

Explaining the trigonometric ratios of right triangles for sine, cosine, and tangent

Using the unit circle to sketch the graph of the cosine function

Using the unit circle to sketch the graph of the sine function

Solving a trig equation with sine and cosine using aPythagorean Identity

Solving a trig equation with sine and cosine using trig identities

Solving a trigonometric equation with sine and cosine by factoring

Writing the sine and cosine functions for a given graph

Finding the exact values of cosine and cotangent for given angles using the unit circle

Finding the exact values of sine and secant for several given angles using the unit circle

Finding the angles where sine has a given value using the unit circle

Finding the angle where secant has a given value and tangent is positive

Using a Double Angle Identity to find the exact value of an expression with sine and cosine

Using the Half-Angle Identities to find the exact values of sine, cosine, and tangent

Using the double angle identities for cosein to derive the half-angle identities for sine and cosine

Interpreting integrals to represent areas between curves

Finding the values of all six trigonometric functions of an angle given a right triangle

Evaluating the other five trigonometric functions for an acute angle given the value of sine

Evaluating the other five trigonometric functions given sine and that tangent is negative

Using trigonometric identities to integrate powers of sine and cosine

Using u substitution to evaluate integrals and prove facts about logarithms and integrals and

Finding a partial fraction decomposition and integrating using partial fractions

Properties and derivatives of inverse trigonometric functions

Properties and derivatives of inverse trigonometric functions

Properties of inverse trig functions and the derivative of arctangent

Converting parametric equations into a Cartesian equation

Finding a Cartesian equation for a parametric curve

Using vectors to find the magnitude and direction of a resultant force

Evaluating compositions of trigonometric and inverse trigonometric functions

Proving trigonometric identities useful for integration

Solving a trigonometric equation with sine and cosine on a given interval

Using trig to find an angle in a right triangle with two given sides

Solving a trig equation with sine and tangent using a trig identity

Solving a trig equation with cosine using trig identities

Finding all solutions to a trigonometric equation with sine

Solving a trigonometric equation with tangent and sine by factoring

Graphing a period of a transformed sine function

Graphing a period of a transformed cosine function

Finding the exact value of tangent for several given angles using the unit circle

Finding the exact value of secant, cosecant, and cotangent using the unit circle

Solving a limit example with a trigonometric functions

Solving a limit example with a trigonometric function

Evaluating a trigonometric limit using trigonometric identities

Proving the derivatives of trigonometric functions and that sine is continuous

Using a rotation map matrix to rotate a 2-dimensional vector by the angle \(\pi\)

Using the Sum and Difference Identities to find the exact value of cosine

Using the Sum Identity for Trig to find the exact value of sine

Proving facts about the derivatives of vector functions including the product rule

Integrating a function with sine using u-substitution

Converting parametric equations into a Cartesian equation and graphing

Evaluating trigonometric functions given a point on the terminal side of an angle

Evaluating all six trigonometric functions for angles in degrees and radians

Evaluating all six trigonometric functions for a right triangle

Evaluating all six trigonometric functions for a right triangle

Using trigonometry to determine the edge lengths of a right triangle

Evaluating trigonometric functions given a point on the terminal side of an angle

Evaluating compositions with inverse trigonometric functions

Evaluating compositions with inverse trigonometric functions

Verifying a trigonometric identity

Verifying a trigonometric identity

Using a sum formula to rewrite a trigonometric expression

Using a double angle formula to solve a trigonometric equation

Using a double angle formula to solve a trigonometric equation

Using double angle formulas to evaluate trigonometric functions

Discussing the degree and radian measure of special angles on the unit circle

Finding the coordinates on the unit circle for all the common angles

Using the Pythagorean Trig Identity to derive the secondary Pythagorean Identities

Finding the coordinates on the unit circle for the common angles in the first quadrant

The coordinates for the quadrantal angles on the unit circle

Finding the six trigonometric ratios for a right triangle

Explaining the special right triangles and the relationships between their sides

Defining radians for angle measure using the corresponding arc length on a unit circle

Drawing an angle in standard position

How to find reference angles for angles in standard position

Explaining the Pythagorean Theorem and using it to find a missing side in a right triangle

Defining coterminal angles and how to determine if angles are coterminal

Tangent lines to parametric equations and related rates examples

Tangent lines to parametric equations and related rates examples

Calculating slopes of tangent lines to parametric curves

Derivatives of exponential and logarithmic functions and the exponential model

Derivatives of exponential and logarithmic functions and the exponential model

Examples involving the tangent line to an exponential function and finding the derivative of hyperbolic cosine

Solving an quadratic-like equation with sine by factoring

Writing a cosine function for a given graph

Implicit differentiation and finding tangent lines

Proving a property of scalar multiplication for limits using the epsilon-delta definition and using the Squeeze Theorem for Limits.

Using trigonometric identities to solve an integral with powers of sine and cosine

Using trigonometric identities to integrate a power of cosine

Using a trigonometric identity to integrate powers of sine and cosine

Using a trigonometric identity to integrate powers of sine and cosine

Using trigonometric identities to integrate even powers of sine and cosine

Using u-substitution on an indefinite integral with an exponential function, sine, and cosine

Mean Value Theorem and properties of a graph

Mean Value Theorem and properties of a graph

Finding the derivative of an implicit function

Finding the derivative of an implicit function

Determining the rate that the area of a triangle is increasing based on the rate an angle is increasing

Using L'Hospital's Rule to solve a limit

Using the Fundamental Theorem of Calculus to find the derivative of a function defined using an integral

Evaluating a definite integral with an exponential and sine function

Using u-substitution to evaluate an indefinite integral

Evaluating a composition of trigonometric and inverse trigonometric functions

Simplifying expressions containing trigonometric and inverse trigonometric functions

Using the Chain Rule to differentiate functions

Using the Chain Rule to differentiate functions with exponential and trigonometric functions

Using the Chain Rule to differentiate a function containing trigonometric functions

Using the Chain Rule to find the pattern for a higher order derivative

Finding the derivative using implicit differentiation

Finding the derivative using implicit differentiation

Finding the derivative using implicit differentiation

Finding the derivative using implicit differentiation

Finding a tangent line to an curve defined implicitly

Finding the derivative of a function containing a logarithmic function

Finding the derivatives of functions containing logarithms

Finding the derivative of a function containing a logarithms

Using logarithmic differentiation to find the derivative of a function

Using logarithmic differentiation to find the derivative of a function

Graphing a vector function by converting it to a Cartesian equation

Finding the tangent line to a parametric curve

Finding a higher order derivative of a function

Using the Product and Chain Rule to find several derivatives

Using the Quotient and Chain Rules to find several derivatives

Using the Product and Chain Rules to differentiate functions with logarithms

Differentiating functions with logarithmic and inverse trigonometric functions

Using the chain rule to find a derivative

Using logarithmic differentiation to find the derivative of a function

Using logarithmic differentiation to find the derivative of a function

Finding where a function has horizontal tangent lines

Finding the absolute maximum and absolute minimum values of a function on a closed interval

Evaluating a limit using L'Hospital's Rule

Finding the antiderivative of a function

Finding a function from its second derivative using antidifferentiation

Antidifferentiating twice to find a function from its second derivative

Antidifferentiating twice to find a function from its second derivative

Antidifferentiating to find a function from its derivative

Antidifferentiating twice to find a function from its second derivative

Finding the antiderivative of a function and using a function value to find the constant

Evaluating a limit with an indeterminant product using L'Hospital's Rule

Cartesian equations and parametric equations of curves

Finding the amplitude, period, phase shift, and vertical shift for a given sine function

Review of vector functions and parametric equations

Implicit differentiation and physics applications of derivatives

Derivatives of parametric equations and tangent lines

Reviewing the chain rule and the derivatives and limits of trigonometric functions

Review of limits and derivatives of inverse trigonometric functions

Review of limits and derivatives of inverse trigonometric functions

Review of trigonometric substitution

Review of sequences and finding the sum of a series

Review of Taylor and Maclaurin Series and their properties

Using Reimann sums and the Fundamental Theorem of Calculus

Using Riemann sums and the Fundamental Theorem of Calculus

Sketching one period of a transformed sine graph

Solving an equation with cosine on a given interval

Solving a trigonometric equation with sine on a given interval

Using trig to find the length of the side of a right triangle given an angle and side length

Using the Even/Odd and Cofunction Identities to solve an equation with sine

Solving a trig equation with cotangent and cosecant using trig identities

Solving a trig equation with cotangent and sine using trig identities

Solving a trigonometric equation with secant by factoring

Finding Taylor and Maclaurin Series for functions

Reviewing Taylor and Maclaurin Series and Taylor's Inequality

Using the reciprocal and ratio trig identities to simplify an expression

Using the Pythagorean Identities to simplify a trig expression

Using the Reciprocal, Ratio, and Pythagorean Identities to verify a trig identity

Proving a trigonometric identity involving secant, cotangent, and tangent

Proving a trig identity involving sine and cosine

Proving a trig identity involving sine, cosine, and cotangent

Integrating using a trigonometric substitution

Derivatives of trigonometric functions and using the Chain Rule

Derivatives of trigonometric functions and using the Chain Rule

Evaluating an integral using trigonometric identities

Evaluating an integral using trigonometric identities

Determining if a series converges or diverges

Converting parametric equations into a Cartesian equation and graphing

Find the integral representing the surface area of a rotated parametric curve

Evaluating a surface integral over a cylinder

Finding the length of a three-dimensional curve

Finding the position vector function given the velocity and an initial position

Finding the angle of intersection for two three-dimensional vector functions

Finding all second-order partial derivatives of a function of two variables

Finding the maximum rate of change and the direction it occurs for a function of two variables

Finding trigonometric functions given information about the angle

Determining the properties of a sine function and graphing it

Writing the equation for a sine function with certain characteristics

Determining the properties of a cosine function and graphing it

Writing the equation for a cossine function with certain characteristics

Writing the equation for a sine function to match a given graph

Writing the equation for a cosine function to match a given graph

Evaluating a double integral over a rectangle

Solving a trigonometric equation

Solving a trigonometric equation by factoring

Solving a trigonometric equation

Solving a trigonometric equation

Solving a trigonometric equation

Using a difference formula to evaluate a trigonometric function

Using a sum formula to evaluate a trigonometric expression

Evaluating a double integral by changing to polar coordinates