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Trigonometry

Browse High School Trigonometry
Stars indicate particularly interesting answers or good places to begin browsing.

Selected answers to common questions:
    DeMoivre's theorem.
    Volume of a tank.



Angles in Trig Functions: Significant Figures [10/05/1999]
Handling significant figures in angle measurements in trigonometry problems.

Another Trig Equation [3/30/1996]
Solve: 4sinx + 3cosx = 4

Answer to a Trig Question [5/1/1995]
What is the range of sin x = 1 / csc x ?

Applications of Non-antidifferentiable Functions [01/29/1999]
What are some of the real life applications of the functions sin (x)/ x, e^(-x^2), and sin (x^2)?

Applications of Trigonometry [07/19/1998]
Can you help me with the following trigonometry questions on: vectors and airspeed, the area of a triangle, and the sixth roots of -64?

Approximating Arcsin [08/10/1999]
Using the Taylor series, a polynomial, or interpolation to calculate arcsin.

Arccos [08/23/1997]
Please solve: Arc cos (cos y) + Arc sin (sin x) = y + x.

Arccos Algorithms and Computer Calculators [03/21/1998]
I need an algorithm to find the arccos of a value.

Arccos(x) + Arcsin(x) = Pi/2 [02/04/2001]
Prove that for all x between -1 and 1, arccos(x) + arcsin(x) = pi/2.

Arc of a Circle [08/16/2003]
I am planning a model railroad, using Lionel section track.

Arcsin, Arccos, Arcsec Are Confusing in their Ranges [12/01/2011]
A student wonders what determines the ranges of inverse trigonometric functions. After listing the general criteria, Doctor Peterson cites several different conventions and motivations, explaining that the definitions often come down to context and convenience.

Arctan and Polar Coordinates [03/09/1999]
What is arctan?

Area of a Cone [11/5/1994]
What is the area of a cone when given the height and the angle at the convergence point?

Area of an Octagonal House [08/24/2003]
I plan to build an octagonal home, and would like to know the area of the completed home if each wall span is 14 feet in length.

Area of an Unusual Hexagon [12/05/1996]
Find the area of a hexagon made from a triangle with squares appended to each of its sides and three more triangles each consisting of one unknown side and two sides which are shared with two of the squares.

Area of a Regular Octagon [10/27/1999]
How do you find the area of a regular octagon?

Area of a Regular Octagon: Proof of a Formula [08/31/1998]
A proof of the formula.

Area of a Triangle [6/2/1996]
Knowing one side measures 1 and two adjacent angles measure a and b...

Area of a Triangle [10/18/2003]
Why can the formula K = a^2*sin(B)*sin(C)/[2*sin(B+C)] be used to compute the area of a triangle?

Area of Intersection of Two Circular Segments [04/20/2007]
Given a circle of radius r and center c, suppose two intersecting chords AB and CD (intersecting in P) form two circular segments. How do I compute the area of the intersection of the two circular segments?

Area of Quadrilateral, Given Angles and Two Opposite Sides [05/13/2002]
If I have a quadrilateral with all the angles known and two opposite sides known, can I find the area?

Art Gallery Problem [11/30/1997]
A picture is two meters high and is hanging so the bottom of the picture is one meter above eye level. How far from the wall should you stand so the angle of vision occupied by the picture is a maximum?

Asin/acos/atan for Complex Numbers [3/27/1996]
How do you find asin(x+iy), acos(x+iy), and atan(x+iy)?

Ballista Equation [09/30/2002]
I have to create an equation for how a ballista, an ancient weapon in the form of a giant crossbow, which fires bolts and grapeshot, would accurately hit its target.

Basic Trig Identities [09/15/1997]
If sin(theta) = 3/4, find sec. I tried the reciprocal identity, but that didn't work.

Bretschneider's Theorem and Cyclic Quadrilaterals [11/30/2000]
Can you prove Bretschneider's Theorem for the area of a quadrilateral? Also, can you show that any quadrilateral with supplementary opposing angles can be inscribed in a circle?

Bridging Trig Identities [06/07/2002]
I've been told that when proving trig identities, you have to choose one side to work on, but I can't get that to work.

Building a Circular Horse Pen [06/16/2002]
My Dad and I are building a round pen for our horse. We have 16 16ft. panels and a 10 ft. gate and a 4ft. gate. (270 ft. total) We want to use a radius and mark the places to dig holes for each post that will support the panels, but we don't know how long the radius should be. Can you help?

Building a Manger [12/03/2001]
Given a base of 11" and two walls 7 1/2' and 6" high, both meeting the base a 90-degree angles, what is the length of the roof and what are the angle measures where the walls meet the roof?

Building a Skateboard Ramp [9/19/1995]
I'm trying to build a skateboard ramp, pyramid with flat top, height one foot, angle of ascent thirty degrees, other angles ninety degrees and sixty degrees.

Calculating Cosine Values Graphically and Algebraically [05/01/1998]
If cos(t) = -2/5, what are cos(-t), sin(pi/2 - t), cos(t + 2pi), and cos(t - 2pi)?

Calculating Sine Without Using the Sine Key or a Table [01/02/2004]
I'm curious what the arithmetic is behind the trig functions. For example, to evaluate sin(48), what math process could I use if I didn't have a calculator?

Calculating the Angle of a Plank [08/22/2001]
Are there any equations that could be used to solve for a plank of known width?

Calculating the Sides of a Right Triangle [2/4/1996]
I need help on how to calculate the length of the opposite side of a right triangle if the length of the adjacent side and the angle measures are known.

Calculators and Trig Functions [12/03/1996]
How do calculators solve trigonometric functions? Is there any way to determine the y value on a graph of the arc subtended by the angle theta?

Catenary and Parabola Comparison [04/06/2004]
What is the difference between a catenary and a parabola? I don't know the difference in shape. Why is the St. Louis arch a catenary and not a parabola?

Catenary Curve [03/30/1999]
Find the vertex of a catenary curve.

A Change of Variables [05/05/2003]
How do I solve int(sin^5(2x)cos(2x)dx) ?

Changes in the Cosine Curve [1/27/1996]
I need information on the changes in the cosine curve, especially on the change in amplitude and the period of revolution and phase shift.

Chords From Inscribed Polygons [07/11/2002]
An regular polygon is inscribed in a circle of known radius. Each side of the octagon is a chord of the circle. What is the length of each chord?

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