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Yearly Archives: 2020
Inverse Trigonometric Functions problems
Hard Inverse Trigonometric Expression Value example question
Evaluate the following Trigonometric Expression:
Solution to this Inverse Trigonometric Expression Value practice problem is provided in the video below!
Rectangle Word Problem with ArcTangent example
A rectangle is 173 meters long and 106 meters high. Find the angle between diagonal and the longer side.
Solution to this Inverse Trigonometric Function word practice problem is provided in the video below!
Trigonometric Equations with Angle Sum, Difference, Multiple, Half-Angle Formulas problems
Trigonometric Equation Double-Angle and Product-To-Sum example
Solve the following Trigonometric Equations using Double-Angle and Product-To-Sum formulas:
sin2θ – sinθ = 0
cosx + cos3x = cos2x
Solution to this Trigonometric Equation Double-Angle Product-To-Sum practice problem is provided in the video below!
Trigonometric Angle Sum, Difference, Multiple, Half-Angle Formulas problems
Trigonometric Angle Sum and Difference example question
Find the value of the following Trigonometric Expressions using Angle Sum or Difference formulas:
cos(105º)
Solution to this Trigonometric Angle Sum Difference practice problem is provided in the video below!
Trigonometric Equations problems
Solution to Trigonometric Equation example question
Solve the following Trigonometric Equations:
tan(3t) = 1
2cos2u = cosu
ln(sinx) = 0
Solution to this Trigonometric Equations practice problem is provided in the video below!
Conversion of Radians, Degrees, Minutes, and Seconds problems
Radian Degree Minute Second Transformation example question
a) Convert the following angle measure given in Radians into Degrees, Minutes and Seconds:
5 Radians
b) Convert the following angle measure in Degrees, Minute and Seconds into Radians:
424o34‘ 24”
Solution to this Angle Measure Radian Degree Minutes Seconds Conversion practice problem is provided in the video below!
Graphing Trigonometric Functions problems
Amplitude Period Phase Shift of Trigonometric Functions example
Find the Amplitude, Period, Phase Shift, and Vertical Shift for each of the following Trigonometric Functions:
Solution to this Trigonometric Function Graph practice problem is provided in the video below!
All Key Features of Trigonometric Functions example problem
For each of the following Trigonometric Functions, find the Amplitude, Period, Frequency, Midline Equation, Phase Shift, Vertical Shift, Horizontal Stretch or Shrink, Vertical Stretch or Shrink, Domain, and Range.
Solution to this Trigonometric Function Graph practice problem is provided in the video below!
GRAPH of Trigonometric Functions example question
Draw a Graph of the following Trigonometric Functions:
Solution to this Graph of Trigonometric Function practice problem is provided in the video below!
Basic Trigonometric Angles and Values problems
Find ANY Known Trigonometric Value by Hand example question
How do you find the values like 
or 
or 
?
There is a way to use the Unit Circle information and fill out your own Table of Values fast!
All you need is to start with sine function values in the interval [0, 
]
Watch the video below with a detailed tutorial and start being a pro at this!
Solution to this Basic Trigonometric Function Values practice problem is provided in the video below!
Linear Functions problems
Linear Function Word Problem example question
It is common that a piece of equipment has a residual value after it has been depreciated over its entire lifetime.
(a) Find the rule for V(t), the value of a piece of equipment, assuming that the value at time t = 0 is Vo and that the value after 20 years is R.
(b) Use the rule to find the value after 12 years of a piece of equipment originally valued at $7500, assuming that it has a residual value after 20 years of $500.
Solution to this Linear Function practice problem is provided in the video below!
Transformation and Graphs of Functions problems
Transformation and Graphs of Functions SKETCHING example question
(a) Describe how the graph of x = f(y) relates to the graph of y = f(x)
(b) Sketch the Graphs of 
and 
Solution to this Transformation and Graph of a Function practice problem is provided in the video below!
Reference Angles problems
Finding Trigonometric Values Using Reference Angles example question
Find the value of the following Trigonometric Expressions using appropriate Reference Angles:
a) sin(120º)
b) 
c) tan(-45º)
d) 
e) sec(240º)
f) 
Solution to this Reference Angle practice problem is provided in the video below!
Trigonometric Functions problems
Find All Six Trigonometric Functions using Rectangular Coordinates or given Angle example question
a) If t is a point on the unit circle with coordinates 
, find the six Trigonometric Functions of t
b) Find the six Trigonometric Functions of 
Solution to this Trigonometric Function practice problem is provided in the video below!
World’s HARDEST Easy Geometry problems
World’s HARDEST Easy Geometry problem example question
The following triangle, 
, shows angle measures in the base angles A and C, as well as line segments 
, 
and 
. Find the measure of angle AED, that is, 
.
Note: Do not use Trigonometry or Calculus to solve this problem
Solution to this World’s Hardest Easy Geometry practice problem is provided in the video below!
Algebraic and Graph Symmetry Test problems
Algebraic Symmetry Test example problem
Determine if any of the following Equations and their respective Graphs have x-axis symmetry, y-axis symmetry, or origin symmetry.
a. 
b. 
Solution to these Algebra Symmetry Tests practice problems is provided in the video below!
Symmetry Test GRAPHING example question
Determine if any of the following Equations and their respective Graphs have x-axis symmetry, y-axis symmetry, or origin symmetry, and then graph each Equation.
a. 
b. 
Solution to these Graphical Symmetry Tests practice problems is provided in the video below!
Rational and Radical Expressions problems
HARD Rational Expression example question
Reduce and Simplify the following Rational Expressions to lowest terms:
a.
b.
c.
d.
Solution to these Rational Expression practice problems is provided in the video below!
HARD Radical Expression example problem
Reduce and Simplify the following Radical Expressions to lowest terms:
a.
b.
c.
d.
Solution to these Radical Expression practice problems is provided in the video below!
Finding Inverse Functions using Algebra & Graphing Techniques problems
Inverse Function Algebra example problem
Determine the Inverse function of the Square Root function provided below:
Solution to this Inverse Function practice problem is provided in the video below!
HARD Inverse Function Algebra Graphing example question
Determine Inverse functions of the following functions:
Solution to this Inverse Function practice problem is provided in the video below!
Exponential Equation problems
Exponential Equations example question
Solve the following Exponential Equation:
Solution to this Exponential Equation practice problem is provided in the video below!
Exponential Equation example problem
Solve the Exponential Equation provided below:
Solution to this Exponential Equation practice problem is provided in the video below!
Exponential Equations example
Find solutions to the given Exponential Equation:
Solution to this Exponential Equation practice problem is provided in the video below!
Quadratic Equations Factoring vs Completing The Square vs Quadratic Formula
Quadratic Equation example question
Solve the following Quadratic Equations by
a) Factoring
b) Completing the Square
c) Quadratic Formula
Solution to these Quadratic Equations practice problem is provided in the video below!
Albert Einstein’s Puzzle
Albert Einstein’s Fish word puzzle
The Englishman lives in the red house.
The Swede keeps dogs.
The Dane drinks tea.
The green house is just to the left of the white one.
The owner of the green house drinks coffee.
The Pall Mall smoker keeps birds.
The owner of the yellow house smokes Dunhills.
The man in the center house drinks milk.
The Norwegian lives in the first house.
The Blend smoker has a neighbor who keeps cats.
The man who smokes Blue Masters drinks bier.
The man who keeps horses lives next to the Dunhill smoker.
The German smokes Prince.
The Norwegian lives next to the blue house.
The Blend smoker has a neighbor who drinks water.
The question to be answered is: Who keeps fish?
Solution to this Puzzle practice problem is provided in the video below!
Orthocenter Outside the Obtuse Triangle problems
Centroid Circumcenter Incenter Orthocenter properties example question
In the following video you will learn how to find the coordinates of the Orthocenter located outside the triangle in the standard xy-plane (also known as coordinate plane or Cartesian plane). In acute and right triangles, the Orthocenter does not fall outside of the triangle. However, when the triangle in question is obtuse, that is, when one of its interior angles measures more than 90 degrees – the Orthocenter will be located outside the triangle. This is when you will need to understand the technique used to find its coordinates.
Solution to this Orthocenter in Obtuse Triangle Geometry practice problem is provided in the video below!
Centroid Circumcenter Incenter Orthocenter problems
Centroid Circumcenter Incenter Orthocenter properties example question
In this video you will learn the basic properties of triangles containing Centroid, Orthocenter, Circumcenter, and Incenter. Then you can apply these properties when solving many algebraic problems dealing with these triangle shape combinations.
Solution to this Centroid Circumcenter Incenter Orthocenter Geometry practice problem is provided in the video below!
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