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Selected answers to common questions:
Volume of a tank.
- Find Height of a Flagpole without Approaching the Pole [04/13/2006]
Points A, B, and C are exactly on level ground, A to B is 80 meters,
the angle at B is a right angle. On C is a vertical flagpole with the
top of the pole = D. Angle CBD = 32 degrees and angle CAD = 24
degrees. What is the height of the flagpole CD?
- Finding a Missing Angle [01/23/2002]
Using trigonometry, calculate the measure of angles ABC and ACB.
- Finding an Angle [08/09/2002]
I need to know how to calculate an angle between two points.
- Finding an Angle between a Line and a Line Segment [10/29/1995]
What is the best way to find the angle between a line and a line segment
that both originate at the same point?
- Finding an Angle Between Tangent Lines [10/19/2003]
How do I find the angle between the tangents to the graphs of y = e^(x)
and y = e^(-x) at the point of intersection?
- Finding Angles [9/6/1996]
Given the side lengths of a right triangle, how do I compute the angle
- Finding Arc Sin [8/13/1996]
How can I use sin, cos, tan, and arctan to define arcsin and arccos?
- Finding a Trig Function of an Angle [07/09/2004]
If sin(y) = 8/17, find cot(y).
- Finding Coordinates [12/31/1996]
Given two intersecting line segments, the angle they form at their
intersection, the coordinates of one endpoint and those of the
intersection, and the length of one of the line segments, how do you
determine the coordinates of the remaining endpoint?
- Finding Intervals in Trig Graphs [10/25/1998]
Can you help me with graphing sine and cosine functions? How do you mark
off the intervals?
- Finding Shareware and Freeware for Teaching Trig [5/13/1995]
Where can I find some shareware or freeware programs for teaching
trigonometry (MS-DOS, Windows, or Mac)?
- Finding Sides and Angles [01/22/2001]
Can you determine the length of the hypotenuse and an acute interior
angle of this right triangle?
- Finding the Adjacent and Opposite Sides in a Right Triangle [06/12/2008]
What is the difference between the adjacent side and the opposite side
and how do I tell which is which?
- Finding the Angle of a Vector [05/10/2000]
How can I find the angle for a vector (x,y) that originates from the
- Finding the Arc Length of a Hanging Catenary [07/23/1997]
A catenary is suspended between two equal poles 400 feet apart at equal
height; it sags in the center 40 feet...
- Finding the Area of a Regular Pentagon [04/15/1998]
How can you find the area of a regular pentagon given only the length of
- Finding the Length of an Arc [2/14/1996]
Find the length of an arc that subtends an angle of measure 70 degrees on
a circle of diameter 15 cm., and find the area of that sector.
- Finding the Period of a Squared Trig Function [08/28/2006]
How do you find the period of a cosine equation when the cosine is
squared, such as y = 3 - 2cos^2[pi(x)/3]?
- Finding the Third Side [04/24/1999]
Using trigonometry, how do you find a third side of a scalene triangle
given two side measures and an angle measure?
- Finding the Value of an Inverse Trig Function [05/08/2000]
How can I find the value of cot[sin^-1(4/5)]?
- Finding Values by Hand [08/26/1998]
How can you find the exact value for sin 18, cos pi/16, etc. without
using a calculator?
- Finding Values of x for Trig Equation [9/11/1996]
How do I find the values of x to make: tan x = -x/((16-x^2)^.5)) true?
- Finding What Number has the Sine of X [4/12/1996]
If the sine of y is x, is there a way to figure out what y is?
- Find the Cities [06/19/2001]
Given the latitudes and longitudes of Detroit, MI, and Miami, FL, find
every city within 10 miles of a straight line between them.
- Formulas for Sine and Cosine [1/24/1996]
What are the formulas for finding sin, cos, and tan in terms of theta?
- Formulas: Width, Side Length of Octagon [03/24/1997]
Given the width of an octagon, what is the length of a side, and vice-versa?
- Fractions and Trig Functions [11/26/2001]
In verifying tan2x-cotx=0, if students approach the problem using
(2tanx)/(1-tan^2x)=1/(tanx) they get only 4 of 6 possible solutions...
- Function Exponentiation Convention [04/21/2013]
A student seeks clarity on the meaning of f^2(x) and other expressions that juxtapose
functions and exponents. Doctor Vogler empathizes, outlining the differing
interpretations, before recommending contextual clues — and pointing up a
larger lesson about ambiguity.
- Function Frequencies [02/03/2001]
Why does the tangent function have twice the frequency of the sine and
- General Strategy for Simplifying Trig Identities and Expressions [12/01/2003]
Simplify sin^2(x) cos^2(x) - cos^2(x).
- Geometry of a Pizza [5/31/1996]
How can you divide a slice in half by cutting across a wedge?
- Given a Triangle with Angles a,b,c [05/03/1999]
Show that cos(a)+cos(b)+cos(c) is less than or equal to 3/2.
- Given Tangent, Find Angle [7/2/1996]
Given tan y=3n/4n, find y.
- Graphing Peculiarity [07/24/2002]
When I use a calculator to graph one form of an equation it works
fine; but when I use a different form, it doesn't work. What's going
- Graphing Polar Equations [06/02/2002]
I need to graph the polar equation (r-3/5)^2 = cos(7 theta), and I
don't know how to do it.
- Graphing Sine and Cosine [07/07/2000]
How do you graph equations that use the sine or cosine functions?
- Graphing Trig Functions [05/03/1997]
How do you graph y = 3sin4x-3?
- Graphing Trig Functions [09/08/2004]
Doctor Ian's method of graphing and calibrating the axes for sine and
cosine curves that involve phase shifts and period changes.
- Graphing Trigonometry Equations [5/15/1996]
How do I graph this one: Sin A - Cos A ?
- Graph of Circle as a Function [05/30/1998]
The graph of a circle is not a function because it fails the vertical
line test. How could you make it a function?