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Trigonometric Form of Complex Numbers problems
Complex Number Trigonometric Form Representation problem example
Express the following Complex Numbers in Trigonometric Form:
-12
-8i
2 – 2i
Solution to this Complex Number Trigonometric Form Representation practice problem is provided in the video below!
Trigonometric Complex Number Product Quotient Power Rectangular Standard Form Representation example question
Find the resulting Complex Number in standard (rectangular) form for the following:
Solution to this Trigonometric Complex Number Product Quotient Power Rectangular Standard Form Representation practice problem is provided in the video below!
Square Roots of a Complex Number example
Find the two Square Roots of
Solution to this Square Roots of a Complex Number practice problem is provided in the video below!
Complex Number Rectangular POLAR Form Conversion example problem
Express the following POLAR Complex Number in Trigonometric and Rectangular Form:
Express the following Rectangular Complex Number in Trigonometric Form and POLAR Form:
5i
Solution to this Complex Number Polar Rectangular Form Conversion practice problem is provided in the video below!
Complex Number POLAR Product Quotient Power example question
Find the resulting Complex Number in POLAR form for the following:
a) 
b) 
Find the resulting Complex Number in POLAR and RECTANGULAR (standard) form:
Solution to this Complex Number Polar Product Quotient Power practice problem is provided in the video below!
POLAR Complex Number Nth Root Theorem example
Find the Four 4th (Fourth) Roots of
Solution to this Polar Complex Number Nth Root Theorem practice problem is provided in the video below!
Force Weight Vector word problems
Horizontal and Vertical Components of a Force Vector problem example
A force of 46.3 pounds is applied at an angle of 34.8º to the horizontal. Resolve the force into horizontal and vertical components.
Solution to this Horizontal Vertical Components of a Force Vector word practice problem is provided in the video below!
HARD Parallel Perpendicular Weight Vector Components to Surface word problem
A weight of 75 pounds is resting on a surface inclined at an angle of 25º to the ground. Find the components of the weight parallel and perpendicular to the surface.
Solution to this Parallel Perpendicular Weight Vector Components word practice problem is provided in the video below!
VERY HARD Resultant Force Vector example question
Find the resultant of two forces, one with magnitude 155 pounds and direction N50ºW, and a second with magnitude 305 pounds and direction S55ºW.
Solution to this Resultant Force Vector word practice problem is provided in the video below!
Law of Cosines problems
Law of Cosines word problem example
Two sides of a parallelogram are 9 and 15 units in length. The length of the shorter diagonal of the parallelogram is 14 units. Find the length of the long diagonal.
Solution to this Law of Cosines word practice problem is provided in the video below!
HARD Law of Cosines word problem
A new car leaves an auto transport trailer for a test drive in the flat surface desert in the direction N47ºW at constant speed of 65 miles per hour. The trailer proceeds at constant rate of 50 miles per hour due East. If the car has enough fuel for exactly 3 hours of riding at constant speed, what is the maximum distance in the same direction that the car can cover in order to safely return to the trailer?
Solution to this Law of Cosines word practice problem is provided in the video below!
Law of Sines problems
Law of Sines word problem example
A radio antenna is attached to the top of the building. From a point 12.5 meters from the base of the building, on level ground, the angle of elevation of the bottom of the antenna is 47.2 degrees and the angle of elevation of the top is 51.8 degrees. Find the height of the antenna.
Solution to this Law of Sines word practice problem is provided in the video below!
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!
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!
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!
Shaded Area in Geometric Figure puzzles
Shaded Area in a Square puzzle example question
In a unit square ABCD, point A is joined to the midpoint of BC, point B is joined to the midpoint of CD, point C is joined to the midpoint of DA, and point D is joined to the midpoint of AB. Find the area of the shaded region.
Solution to this Puzzle practice problem is given in the video below!
Shaded Area in a Square puzzle example problem
In a unit square ABCD, M is a midpoint of AD, and AC is a diagonal. Find the area of the shaded regions.
Solution to this Puzzle practice problem is given in the video below!
Shaded Area in a Square puzzle example
In the unit square ABCD, M is the midpoint and AC and BD are diagonals. Find the area of the shaded region.
Solution to this Puzzle practice problem is given in the video below!
Shaded Area in a Square puzzle example question
In the following unit square ABCD, M is the midpoint and BD is a diagonal. Find the area of the shaded region.
Solution to this Puzzle practice problem is given in the video below!
Shaded Area in a Square puzzle TRIGONOMETRY example problem
A square with side 1 is rotated around one vertex by an angle 
, where
and
.
Find the area of the shaded region.
Solution to this Puzzle practice problem is given in the video below!
Shaded Area in a Rectangle puzzle example
In the following rectangle, an isosceles triangle is drawn. Find the area of the shaded region.
Solution to this Puzzle practice problem is given in the video below!
Shaded Area in a Rectangle puzzle example question
In the following rectangle below, find the area of the shaded region.
Solution to this Puzzle practice problem is given in the video below!
Polar Coordinates problems
Polar Rectangular Coordinates Conversion example question
Convert the following Rectangular coordinates to Polar coordinates:
a. (2, -2)
b. (0, 3)
c. (3, 4)
Solution to this Polar Coordinates practice problem is given in the video below!
Rectangular Polar Coordinates Conversion example problem
Convert the following Polar coordinates to Rectangular coordinates:
a. 
b. (0, 3)
c. 
Solution to this Polar Coordinates practice problem is given in the video below!
Rectangular Polar Coordinates Conversion example
Convert the following Polar coordinates to Rectangular coordinates:
a. 
b. 
c. 
Solution to this Polar Coordinates practice problem is given in the video below!
Rectangular Equation & Polar Equation Conversion example question
Find Polar Equations from Rectangular Equation
Solution to this Polar Coordinates practice problem is given in the video below!
Polar Equations Sketch & X–Y Equation Conversion example problem
Sketch the given Polar Equations and find their corresponding X–Y Equation:
a. r = 4
b. 
c. 
d. 
Solution to this Polar Coordinates practice problem is given in the video below!
Hard Polar Equations Sketch example
Sketch the given Polar Equations:
Solution to this Polar Coordinates practice problem is given in the video below!
Parametric Equation problems
Parametric Equation Sketch & X–Y Equation Conversion example question
Sketch the given Parametric Equation and find its corresponding X–Y Equation:
Solution to this Parametric Equations & Curves practice problem is given in the video below!
Parametric Equation Sketch & X–Y Equation Conversion example problem
Sketch the given Parametric Equation and find its equivalent X–Y Equation:
Solution to this Parametric Equations & Curves practice problem is given in the video below!
Parametric Equation Sketch & X–Y Equation Conversion example
Find Parametric Equations from the given X–Y equation:
Circle with radius 3, centered at (2, 1) and drawn counterclockwise.
Solution to this Parametric Equations & Curves practice problem is given in the video below!
Parametric Equation Sketch & X–Y Equation Conversion example question
Derive Parametric Equations from the given X–Y equation:
Line from (-2, 4) to (6, 1).
Solution to this Parametric Equations & Curves practice problem is given in the video below!
Parametric Equation Sketch & X–Y Equation Conversion example problem
Find Parametric Equations by using the given X–Y equation:
from (2, -2) to (0, 2).
Solution to this Parametric Equations & Curves practice problem is given in the video below!
Parametric Equations: Points of Intersection of Two Curves example
Find the coordinates of the points of Intersection of two given Parametric Curves:
Solution to this Parametric Equations & Curves practice problem is given in the video below!
Parametric Equations: Object Position, Velocity & Speed example question
Find the Position, Velocity and Speed of an Object by using the following Parametric Equation:
Solution to this Parametric Equations & Curves practice problem is given in the video below!
Slope of the Parametric Curve example problem
Find the Slope of the Tangent Line to the Curve
Solution to this Parametric Equations & Curves practice problem is given in the video below!
Parametric Curves: Coordinates of the Points of Vertical & Horizontal Tangent Lines example
Find the Coordinates of the Points of Vertical and Horizontal Tangent Lines to the Curve
Solution to this Parametric Equations & Curves practice problem is given in the video below!
Parametric Curves: Arc Length example question
Find the Arc Length of a Parametric Curve
Solution to this Parametric Equations & Curves practice problem is given in the video below!
Parametric Curves: Area example problem
Find the Area enclosed by a Parametric Curve
in the interval
Solution to this Parametric Equations & Curves practice problem is given in the video below!
Conic Section Proof problems
Parabola Directrix Conic Section Proof example question
Show that in polar coordinates the equation of a conic section with (one) focus at the pole and directrix,
the line
can be written as
.
Solution to this Conic Section Proof practice problem is given in the video below!
Trigonometric Identity Proof problems
Trigonometric Identity Proofs example problem #1
Show that
Solution to this Trigonometric Identity Proof practice problem is given in the video below!
Trigonometric Identity Proof example question #2
Show that the following equation is valid.
Solution to this Trigonometric Identity Proof practice problem is given in the video below!
Trigonometric Identity Proofs example #3
Prove the validity of the following equation.
Solution to this Trigonometric Identity Proof practice problem is given in the video below!
Trigonometric Identity Proof example problem #4
Prove that
Solution to this Trigonometric Identity Proof practice problem is given in the video below!
Trigonometric Identity Proofs example question #5
Prove the following identity.
Solution to this Trigonometric Identity Proof practice problem is given in the video below!
Trigonometric Identity Proof example #6
Show that the following identity holds.
Solution to this Trigonometric Identity Proof practice problem is given in the video below!
Trigonometric Identity Proofs example problem #7
Prove the following identity.
Solution to this Trigonometric Identity Proof practice problem is given in the video below!
Trigonometric Identity Proof example question #8
Verify the given identity.
Solution to this Trigonometric Identity Proof practice problem is given in the video below!
Trigonometric Identity Proofs example #9
Show that the identity given below is valid.
Solution to this Trigonometric Identity Proof practice problem is given in the video below!
Trigonometric Identity Proof example problem #10
Verify the given three Trigonometric Identities:
(a) 
(b) 
(c) 
Solution to this Trigonometric Identity Proof practice problem is given in the video below!
Trigonometry problems (complete Playlist)
Find comprehensive Trigonometry examples and practice problems found in your Calculus or Precalculus courses.
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