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Selected answers to common questions:
Volume of a tank.
- Inverse Trig Functions and Special Angles [01/25/2006]
Find the exact value of the expression arctan(sqrt(3)). I know this
means the angle with a tangent of sqrt(3) but how do I figure out that
angle without a calculator?
- Inverse Trigonometric Ratios [07/01/2003]
Why aren't the inverse trigonometric ratios equal to 1/(the ratio),
as is the case for numbers?
- Inverse Trigonometry [08/22/2001]
I can't find my mistake.
- Irregular Sinusoidal Curves [08/24/2004]
Can you create a sinusoidal function with a fixed period such that the
time span between the max and min is not the same as the time span
between the min and max?
- Land Plot Area [08/28/2002]
I have a parcel of land. The surveyor has determined it to be
624,630.88 square ft. and 14.340 acres. The legal description is 15.8
acres. How can I figure out the square footage?
- Law of Cosines and Pythagorean Theorem [09/23/1997]
I would like to know how to calculate the angles in a triangle if all you
know is the length of the three sides.
- Law of Cosines in Informal Trigonometric Proof [12/22/2004]
If cosA/cosB = b/a, then show that triangle ABC is either isosceles
- Law of Tangents [01/22/1999]
What is the law of tangents? How is it derived?
- Laws of Sines and Cosines [03/07/2002]
When I set up the problem, the three angles don't add up to 180 degrees.
- Length of a Triangle's Sides [1/23/1995]
I have a triangle problem for you to solve: The lengths of the three
sides of a triangle could be...
- Length of the Diagonals of a Parallelogram [05/22/2000]
A parallelogram has a 70-degree angle and sides 6cm and 10cm long. How
long are its diagonals?
- Limit of Cos(Cos( ... Cos(x) ... ))) [02/24/2001]
Find the limit of a repeating trigonometric expression cos(cos( ...
cos(x) ... )) as the number of cosines goes to infinity.
- Location of Plane Flying on Great Circle [11/20/2003]
An aircraft flies from 60°N 030°W to 60°N 030°W following a great
circle. When 025°W is passed, what will the plane's latitude be?
- Logarithmic Equivalent of the Inverse Hybolic Cosine Function [10/28/1997]
I recently attempted a question which I think I have done wrong and I was
wondering if there were a set formula for this problem...
- Maximizing Horizontal Distance [04/10/1998]
Using algebra, prove that an object needs to be thrown at 45 degrees to
travel the greatest possible horizontal distance.
- Mean Latitude/Longitude [07/10/2003]
Given three points on the earth measured in latitude/longitude, what
is the formula to calculate a mean latitude/longitude for this group
- Meteoric Reprise [10/22/2016]
An adult sees a meteor, and wonders how close it came. With two applications of
trigonometry laws, Doctor Rick compiles a table of distances.
- Methods of Computing Trig Functions [09/07/99]
What would I do to figure out the actual angle of C, without using a
table or calculator, if I know that tan(C) = 4/3?
- Miter Angle of a Pipe [02/10/1999]
Find the miter angle of a pipe of certain shape.
- Mitres on Pyramids [09/26/2002]
I am weatherproofing my home, and have to mitre boards in a pyramid
with a rectangular - not square - base, and an apex that is directly
over the centre of one edge of the base.
- Mnemonic For Remembering Formulas for Sin, Cos, Tan [05/15/1998]
The story of Chief Soh Cah Toa.
- Modeling How Much Wood Expands [09/21/2013]
A flooring inspector seeks to quantify how much wood buckles as it expands. Drawing
on trigonometric approximations, Doctors Rick and Peterson each provide heuristics
for this real world problem.
- Modeling Tides with Trigonometry [03/07/2001]
How can I find a trigonometric equation that models the depth of the
water at the end of a pier throughout the day, given the heights and
times of low and high tide?
- Movement on a Sphere, Charted on a Spreadsheet [11/20/2010]
A student seeks help coding a spherical navigation spreadsheet program. Doctor Vogler helps him
develop an algorithm that accounts for the trigonometry involved, with each drawing
on archived conversations.
- Moving a Circle on a Polar Graph [05/04/2001]
How do you move a circle so the center is not (0,0), but to where the
center can be (r,[theta])?
- Multiplying Large Numbers Using Sine and Cosine [12/17/2002]
I am researching Tycho Brahe and have come upon an example where he
uses [sin(a + b) + sin(a - b)]/2 to multiply large numbers together
due to the availability of sine tables. Can you explain the method?
- Non-negative Acute Angle [01/26/1999]
How can you express the sine or cosine of any angle as the sine or cosine
of a non-negative acute angle? Why would they be equal?
- Obtuse Angles Function [08/04/2014]
A student wonders why the relationship between trigonometric functions and triangle
side ratios holds not just for right triangles, but for all triangles. Doctor Peterson models the trigonometry of a non-acute vertex by re-drawing it on the Cartesian coordinate system.
- Octagon Formula [07/30/1997]
If you're building an octagon on a 12-foot radius, what is the length of
- Octagon Side Lengths [08/22/2001]
If I know that the dimension of an octagon from one side to the other is
8 feet, how can I find the lengths of a side?
- One- and Two-sided Polygons [12/07/1999]
Can you explain what a monogon and a digon are?
- Optimization: Minimum Area [11/07/1997]
How do you fold a piece of paper (rect. with width a and unlimited
length) so one corner just reaches the righthand side for minimum area?
- Ordering Products, Powers, and Parameters of Trigonometric Functions [10/31/2010]
A student wants to know how to unambiguously interpret strings of trigonometric
functions, multiplication, and exponentiation. Doctor Peterson digs into a history book
-- as well as another math doctor's conversation -- to illuminate the vagaries of the
- Origin of Radians [05/27/2002]
Where, exactly, did radians come from?
- Origin of the Terms Sine and Cosine [07/02/1997]
I assume the term tan comes from the word tangent, but where do the terms
sine and cosine come from?
- Origin of the Terms Sine, Cosine, Tangent, etc. [10/27/1999]
Can you tell me the origin of the terms hypotenuse, sine, cosine, and
tangent? Can you tell me how the trigonometric formulas for sine, cosine,
and tangent came about?
- Over the Right Field Fence [04/11/1998]
What would be the distance of a hit from home base over the top of a 30
ft. high right field fence?
- Packing 4 Spheres Into a Tetrahedron [09/03/99]
How can I find the dimensions of the smallest tetrahedron that can serve
as a container for 4 spheres packed as snugly as possible?
- Pendulum Altitude [09/26/2002]
A pendulum 45cm long swings through a vertical angle of 30 degrees.
Find the distance of the altitude through which the pendulum bob
- Perimeter of an Inscribed Regular Polygon [12/10/1998]
What is the formula for the perimeter of a regular polygon inscribed
inside a circle?