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Resources tagged with Sine similar to Roots and Coefficients:

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Broad Topics > Trigonometry > Sine

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Complex Sine

Stage: 5 Challenge Level: Challenge Level:3 Challenge Level:3 Challenge Level:3

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.

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Three by One

Stage: 5 Challenge Level: Challenge Level:1

There are many different methods to solve this geometrical problem - how many can you find?

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Trigonometric Protractor

Stage: 4 Challenge Level: Challenge Level:2 Challenge Level:2

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

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Strange Rectangle 2

Stage: 5 Challenge Level: Challenge Level:1

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

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8 Methods for Three by One

Stage: 4 and 5 Challenge Level: Challenge Level:2 Challenge Level:2

This problem in geometry has been solved in no less than EIGHT ways by a pair of students. How would you solve it? How many of their solutions can you follow? How are they the same or different?. . . .

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Pumping the Power

Stage: 5 Challenge Level: Challenge Level:2 Challenge Level:2

What is an AC voltage? How much power does an AC power source supply?

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Moving Squares

Stage: 4 Challenge Level: Challenge Level:2 Challenge Level:2

How can you represent the curvature of a cylinder on a flat piece of paper?

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Figure of Eight

Stage: 4 Challenge Level: Challenge Level:3 Challenge Level:3 Challenge Level:3

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 ?

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Belt

Stage: 5 Challenge Level: Challenge Level:1

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.

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Octa-flower

Stage: 5 Challenge Level: Challenge Level:1

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?

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Small Steps

Stage: 5 Challenge Level: Challenge Level:1

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

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Round and Round a Circle

Stage: 4 Challenge Level: Challenge Level:1

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

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Sine and Cosine for Connected Angles

Stage: 4 Challenge Level: Challenge Level:2 Challenge Level:2

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.

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Ball Bearings

Stage: 5 Challenge Level: Challenge Level:2 Challenge Level:2

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.

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Over the Pole

Stage: 5 Challenge Level: Challenge Level:1

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.

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Sine and Cosine

Stage: 4 Challenge Level: Challenge Level:1

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?

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Degree Ceremony

Stage: 5 Challenge Level: Challenge Level:1

What does Pythagoras' Theorem tell you about these angles: 90°, (45+x)° and (45-x)° in a triangle?

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A Scale for the Solar System

Stage: 4 Challenge Level: Challenge Level:1

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

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The Dodecahedron

Stage: 5 Challenge Level: Challenge Level:3 Challenge Level:3 Challenge Level:3

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?

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After Thought

Stage: 5 Challenge Level: Challenge Level:1

Which is larger cos(sin x) or sin(cos x) ? Does this depend on x ?

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Squ-areas

Stage: 4 Challenge Level: Challenge Level:3 Challenge Level:3 Challenge Level:3

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. . . .

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Sine Problem

Stage: 5 Challenge Level: Challenge Level:1

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.