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Resources tagged with Cosine similar to Pythagoras on a Sphere:

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Broad Topics > Trigonometry > Cosine

Pythagoras on a Sphere

Stage: 5 Challenge Level:

Prove Pythagoras' Theorem for right-angled spherical triangles.

After Thought

Stage: 5 Challenge Level:

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

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 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.

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?

Three by One

Stage: 5 Challenge Level:

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

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. . . .

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?

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?

Cosines Rule

Stage: 4 Challenge Level:

Three points A, B and C lie in this order on a line, and P is any point in the plane. Use the Cosine Rule to prove the following statement.

Far Horizon

Stage: 4 Challenge Level:

An observer is on top of a lighthouse. How far from the foot of the lighthouse is the horizon that the observer can see?