Objectives:

• Use the Pythagorean Theorem to solve for an unknown side of a right triangle.

A good description of the Pythagorean Theorem along with multiple application problems. 

https://www.youtube.com/watch?v=d8EA5TxGzcY

Objectives:

• Recite and use side-length relationships for 45-45-90 and 30-60-90 triangles

Solving 45-45-90 and 30-60-90 triangles 

https://www.youtube.com/watch?v=Y_qs4cgxbgs

Objectives:

• Define and evaluate the six trigonometric functions of acute angles on right triangles given side lengths

• Use a calculator to evaluate trigonometric functions given acute angles in degrees

• Find side lengths of a triangle

• Solve a triangle

Finding all six trigonometric functions of acute angles given sides on the right triangle. 

https://www.youtube.com/watch?v=1T8GTY4_gzo

Finding trigonometric functions using a calculator.

https://www.youtube.com/watch?v=W0fBQM8YC-Q

How to solve a right triangle. 

https://www.youtube.com/watch?v=a5WQlcFTXyk

Objectives:

• Apply skills of solving a triangle

• Apply skills involving bearings, headings, angles of elevation, and angles of depression

This video provides example problems involving trigonometric functions. 

https://www.youtube.com/watch?v=uyKvSe6Ltgs

Objectives:

• Sketch an angle in standard position

• Identify positive and negative angles

• Measure an angle in degrees

• Identify the quadrant of an angle

• Define and identify acute, obtuse, right, straight, and reflex angles

• Identify if two angles are complementary or supplementary

• Find the complement or supplement of an angle

https://www.youtube.com/watch?v=7iBc5bJdanI

Objectives:

• Convert between decimal degrees and DMS

https://www.youtube.com/watch?v=kbN93Q82IB4

https://www.youtube.com/watch?v=UtgAAy-XvCQ

Objectives:

• Define a radian

• Convert between degrees and radians

• Convert between degrees or radians and revolutions

https://www.youtube.com/watch?v=nAJqXtzwpXQ

Objectives:

• Identify if two angles are coterminal

• Given an angle, calculate a coterminal angle that is more positive or more negative

https://www.youtube.com/watch?v=Xtk1PVRoDLQ

Objectives:

• Convert between arc length, angles, and radii

• Convert between linear and angular speeds

• Convert between angles, radii, and sector area

Good quick explanations of finding arc length, linear and angular speeds, and sector areas. 

https://www.youtube.com/watch?v=CrtlRcI2d9U

https://www.youtube.com/watch?v=0YNT4WPLf2E

https://www.youtube.com/watch?v=8-Co_nx7gUg

Objectives:

• Draw and label the unit circle, labeling angles every 45 degrees and 30 degrees

• Label angles every (pi/4) and (pi/6) radians on the unit circle

• Define a reference angle

• Find a reference angle given any angle

• Define the six trigonometric functions on the unit circle

• Calculate the six trigonometric functions on the special angles

These are two important videos that help to extend the concept of trigonometric functions from the triangle to the circle. 

https://www.youtube.com/watch?v=uu2nJEbap80

https://www.youtube.com/watch?v=gUdksdjuSCk

Good video on the use of reference angles to find trigonometric functions using reference angles. 

https://www.youtube.com/watch?v=V8LEHEzdU2U

These videos do the best job of defining reference angles and showing how to figure out the unit circle. 

https://www.youtube.com/watch?v=dBN7wFrebwY

https://www.youtube.com/watch?v=iHa8f7k4Tg8

This last video does the best job of compiling the unit circle.  Watch this as you are assembling your unit circle on your own paper. 

https://www.youtube.com/watch?v=IYHbhaGVI0U

Objectives:

• Evaluate all six trig functions of any angle on the unit circle using a calculator given degrees or radians

This video shows how to find trigonometric functions of acute angles using the calculator.  The procedure is identical for angles not between zero and 90 degrees.  for To do the same with radians, convert to degrees or place your calculator in "radian" mode! 

https://www.youtube.com/watch?v=W0fBQM8YC-Q

Objectives:

• Evaluate all other trig functions given a single trig function and a quadrant

• Calculate trigonometric functions from a point on the terminal side.

• Evaluate trigonometric functions given the equation of a line through the origin

Good, quick video on how to find all trig functions, given a single trig function plus a constraint. 

https://www.youtube.com/watch?v=ftV2e2APCRA

Good discussion on calculating trigonometric functions from a point on the terminal side. 

https://www.youtube.com/watch?v=6HVE6rP5FQQ

Similarly solid discussion, here describing the calculation of trig functions from the equation of a line through the origin. 

https://www.youtube.com/watch?v=vPw4BnoXHSc

Objectives:

• Define the domain of various trig functions

• Define a periodic function

• Define the period of sine and cosine

• Evaluate sine and cosine functions using the period as an aide

Good discussion of the domain of sine and cosine. 

https://www.youtube.com/watch?v=xZ5t9wK42l8

Good discussion of the period of sine and cosine. 

https://www.youtube.com/watch?v=yZLeN_9jjGg

Objectives:

• Identify which trig functions are even or odd

• Use the even and odd properties to help evaluate trig functions

This video gives a good introduction to even and odd trigonometric functions, and using the evenness and oddness of a function as an aid in evaluating their values. 

https://www.youtube.com/watch?v=5p8hokJ3Cqo

Objectives:

• Recite reciprocal, quotient, and Pythagorean identities

• Use reciprocal, quotient, and Pythagorean identities

Great, funny video that introduces all the fundamental trigonometric identities. 

https://www.youtube.com/watch?v=9z5V0Kf7vDg

This video reinforces the fundamental trigonometric identities and introduces the process of proving an identity. 

https://www.youtube.com/watch?v=tvpOM17HhAA

This video gives additional practice for proving identities. 

https://www.youtube.com/watch?v=EnY1-UT-JyE

Objectives:

• Graph elementary sine and cosine curves

• Graph sine and cosine curves with arbitrary amplitudes

• Graph sine and cosine curves with arbitrary frequencies/periods

• Graph sine and cosine curves with arbitrary phase shifts

• Graph sine and cosine curves with arbitrary amplitudes, frequencies, and phase shifts

• Graph sine and cosine curves with horizontal translations

• Graph sine and cosine curves with vertical translations

• Write a trigonometric equation given an amplitude, phase shift, and vertical translation

• Find a trigonometric model to represent a graph

Good discussion of graphing sine and cosine functions, with all their possible transformations.  This instructor uses  `h` and `k`  for his horizontal and vertical offsets.  In class we use different letters for these. 

https://www.youtube.com/watch?v=U3ktjhKRdng

Objectives:

• Graph a tangent function

• Graph a tangent function with arbitrary amplitude and frequency

• Graph a cotangent function

• Graph a cotangent function with arbitrary amplitude and frequency

• Graph a reciprocal function

• Graph a reciprocal function with arbitrary amplitude, frequency, and phase shift

• Graph damped sine waves

• Determine the domain, range, and period of all trig functions

Good explanation of the graph of the tangent function. 

https://www.youtube.com/watch?v=FK6-tZ5D7xM

This video expands the previous video to include the tangent function with a phase shift and a different period. 

https://www.youtube.com/watch?v=3cvWRFT7iWM

This video provides a good review of previous functions, but then extends these to the graphing of secant, cosecant, and cotangent. 

https://www.youtube.com/watch?v=-nr5KCitdGw

Objectives:

• Define the inverse sine, cosine, and tangent function

• Evaluate an inverse sine, cosine, and tangent function for a seminal angle

• Evaluate an inverse sine, cosine, and tangent function using a calculator

• Graph an inverse sine, cosine, and tangent function

• Describe the domain and range of inverse sine, cosine, and tangent functions

• Evaluate compositions of inverse trig functions

• Evaluate compositions of non-inverse trig functions

• Write an equivalent algebraic expression for a composition of trig functions

https://www.youtube.com/watch?v=YXWKpgmLgHk

https://www.youtube.com/watch?v=2ZHN2k9wmAs&list=PL0G-Nd0V5ZMo1g53_xKoo_u_Lt2B9POh0

https://www.youtube.com/watch?v=tQeqXmD_Fho

Objectives:

• Apply skills involving simple harmonic motion

Very comprehensive discussion on the application of trig functions to oscillatory motion. 

https://www.youtube.com/watch?v=sIkcCFhbjVk

The learners will

• Evaluate trigonometric functions

• Simplify trigonometric equations

• Develop additional trigonometric identities

• Solve trigonometric equations

These videos are great sources of more practice for working with trig identities. 

https://www.youtube.com/watch?v=KlM76clMlD4

https://www.youtube.com/watch?v=4YSI8fm4gRQ

Objectives:

The learners will use a variety of techniques to verify trigonometric identities.

Good comprehensive description of the full set of strategies in verifying a trigonometric identity. 

https://www.youtube.com/watch?v=Rf05H8ogHLg

Objectives:

• The students will solve trigonometric equations by -- 

  • collecting like terms,

  • extracting square roots,

  • factoring,

  • using techniques of quadratic equations,

  • rewriting trigonometric equations so that only one trig function is used,

  • squaring both sides and treating it as a quadratic equation, and

  • using inverse functions

• Students will also solve trigonometric equations involving multiples or fractions of an angle

These two videos give a good introduction into solving trigonometric equations. 

https://www.youtube.com/watch?v=sp8MJEWClkY

https://www.youtube.com/watch?v=jKrGXVBuniw

Objectives:

• Students will use trigonometric sum and difference identities to:

  • simplify trigonometric expressions

  • evaluate trigonometric functions

Good introduction to the use of the sum and difference identities for sine, cosine, and tangent. 

https://www.youtube.com/watch?v=liSgx_72bfg

Objectives:

• Students will use double and half-angle formulas to assist in simplifying trigonometric expressions, evaluating trigonometric functions, and solving trigonometric equations.

Good (and funny) demonstration of the double-angle formulas. 

https://www.youtube.com/watch?v=Zcy6JVICWc8

Same for the half-angle formulas. 

https://www.youtube.com/watch?v=ytZvNrdd7U4

Good, quick explanation of how to use the power-reduction formulas. 

https://www.youtube.com/watch?v=4bP1FuASneY

Objectives:

• Use sum-to-product and product-to-sum identities to simplify trigonometric expressions

Good description of how to use the product-to-sum and sum-to-product identities. 

https://www.youtube.com/watch?v=uUh2B9hnI_U

Objectives:

• The students will:

  • Use the Law of Sines to solve non-right triangles

  • Use the Law of Sines to solve real-world problems

  • Find the area of any triangle

Good comprehensive discussion on the use of the Law of Sines to solve triangles. 

https://www.youtube.com/watch?v=9fS0uA4iLxI

Objectives:

• The students will

  • Use the Law of Cosines to solve non-right triangles

  • Use the Law of Cosines to solve real-world problems

  • Find areas of triangles using Heron's Area Formula

An example of using the Law of Cosines when given a triangle with two sides known as well as the included angle in between them. 

https://www.youtube.com/watch?v=ZElOxG7_m3c

This example uses the Law of Cosines to find one of the angles in a triangle where all three sides are known. 

https://www.youtube.com/watch?v=ckyFhQLrq8U

Good discussion of how to find the area of a triangle using Heron's Formula. 

https://www.youtube.com/watch?v=Pi56pFy-8HU

Objectives:

• The learners will:

  • Represent vectors as directed line segments

  • Write the component forms of vectors

  • Perform basic vector operations and represent them graphically

  • Write vectors as linear combinations of unit vectors

  • Find the direction angles of vectors

  • Use vectors to model and solve real-life problems

Good discussion of vectors and components. 

https://www.youtube.com/watch?v=iXdMpXMuEGI

Good discussion of unit vectors. 

https://www.youtube.com/watch?v=jCkhbKFZgLk

Good discussion of how to calculate the direction angle of a vector. 

https://www.youtube.com/watch?v=8Eur16foTMw

This section is a review of concepts described in section 2.4 in the following course:

https://www.determinedparents.com/home/mat1340

This section is a review of concepts described in section 2.5 in the following course:

https://www.determinedparents.com/home/mat1340

Objectives:

• The students will be able to:

  • Find the absolute value (or magnitude) of a complex number

  • Convert a complex number from standard form to its trigonometric form and back again

  • Multiply and divide complex numbers, and understand what happens rotationally in the complex plane when we do this

Good description of how to convert to and from the trigonometric form of a complex number. 

https://www.youtube.com/watch?v=7z9NMWDUhUQ

Good description of how to multiply and divide complex numbers in trigonometric form. 

https://www.youtube.com/watch?v=lhI8H7hJ7pQ