Search by Topic

Resources tagged with Sine similar to Complex Rotations:

Filter by: Content type:
Stage:
Challenge level:

There are 23 results

Broad Topics > Trigonometry > Sine

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.

Three by One

Stage: 5 Challenge Level:

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

8 Methods for Three by One

Stage: 4 and 5 Challenge Level:

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?. . . .

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.

Trigonometric Protractor

Stage: 4 Challenge Level:

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

Pumping the Power

Stage: 5 Challenge Level:

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

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.

Round and Round a Circle

Stage: 4 Challenge Level:

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

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.

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?

Moving Squares

Stage: 4 Challenge Level:

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

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.

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?

Degree Ceremony

Stage: 5 Challenge Level:

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

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.

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?

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?

Where Is the Dot?

Stage: 4 Challenge Level:

A dot starts at the point (1,0) and turns anticlockwise. Can you estimate the height of the dot after it has turned through 45 degrees? Can you calculate its height?

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. . . .

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.

After Thought

Stage: 5 Challenge Level:

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

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.