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Resources tagged with Sine similar to How Many Geometries Are There?:

Other tags that relate to How Many Geometries Are There?

Spheres. 2D representations of 3D shapes. Arcs, sectors and segments. Angles between lines & planes. Limits. Sine. Angles. Circumferences. Non Euclidean Geometry. Geodesics.

There are 21 results

Over the Pole

Stage: 5 Challenge Level:

Two places are diametrically opposite each other on the same line of latitude. Compare the distances between them travelling along the line of latitude and travelling over the nearest pole.

Belt

Stage: 5 Challenge Level:

A belt of thin wire, length L, binds together two cylindrical welding rods, whose radii are R and r, by passing all the way around them both. Find L in terms of R and r.

Small Steps

Stage: 5 Challenge Level:

Two problems about infinite processes where smaller and smaller steps are taken and you have to discover what happens in the limit.

Octa-flower

Stage: 5 Challenge Level:

Join some regular octahedra, face touching face and one vertex of each meeting at a point. How many octahedra can you fit around this point?

Sine Problem

Stage: 5 Challenge Level:

In this 'mesh' of sine graphs, one of the graphs is the graph of the sine function. Find the equations of the other graphs to reproduce the pattern.

Round and Round a Circle

Stage: 4 Challenge Level:

Can you explain what is happening and account for the values being displayed?

Complex Sine

Stage: 5 Challenge Level:

Solve the equation sin z = 2 for complex z. You only need the formula you are given for sin z in terms of the exponential function, and to solve a quadratic equation and use the logarithmic function.

The History of Trigonometry- Part 1

Stage: 2, 3, 4 and 5

The first of three articles on the History of Trigonometry. This takes us from the Egyptians to early work on trigonometry in China.

Sine and Cosine for Connected Angles

Stage: 4 Challenge Level:

The length AM can be calculated using trigonometry in two different ways. Create this pair of equivalent calculations for different peg boards, notice a general result, and account for it.

Figure of Eight

Stage: 4 Challenge Level:

On a nine-point pegboard a band is stretched over 4 pegs in a "figure of 8" arrangement. How many different "figure of 8" arrangements can be made ?

Strange Rectangle 2

Stage: 5 Challenge Level:

Find the exact values of some trig. ratios from this rectangle in which a cyclic quadrilateral cuts off four right angled triangles.

Ball Bearings

Stage: 5 Challenge Level:

If a is the radius of the axle, b the radius of each ball-bearing, and c the radius of the hub, why does the number of ball bearings n determine the ratio c/a? Find a formula for c/a in terms of n.

Sine and Cosine

Stage: 4 Challenge Level:

The sine of an angle is equal to the cosine of its complement. Can you explain why and does this rule extend beyond angles of 90 degrees?

Three by One

Stage: 5 Challenge Level:

NRICH has always had good solutions from Madras College in St Andrew's, Scotland but the solutions to this problem were truly exceptional.

Degree Ceremony

Stage: 5 Challenge Level:

What does Pythagoras' Theorem tell you about these angles: 90°, (45+x)° and (45-x)° in a triangle? Find sin^2 1° + sin^2 2° + ... + sin^2 359 ° + sin^2 360°.

A Scale for the Solar System

Stage: 4 Challenge Level:

The Earth is further from the Sun than Venus, but how much further? Twice as far? Ten times?

8 Methods for Three by One

Stage: 5

Two 18 year old students from Madras College St Andrews in Scotland produced eight different proofs of one result using (separately) Tan Angle Sum Formula, Sin Angle Sum Formula, Cosine Rule,. . . .

Squ-areas

Stage: 4 Challenge Level:

Three squares are drawn on the sides of a triangle ABC. Their areas are respectively 18 000, 20 000 and 26 000 square centimetres. If the outer vertices of the squares are joined, three more. . . .

Trigonometric Protractor

Stage: 4 Challenge Level:

An environment that simulates a protractor carrying a right- angled triangle of unit hypotenuse.

The Dodecahedron

Stage: 5 Challenge Level:

What are the shortest distances between the centres of opposite faces of a regular solid dodecahedron on the surface and through the middle of the dodecahedron?