Search by Topic

Filter by: Content type:
Stage:
Challenge level: Challenge Level:1 Challenge Level:2 Challenge Level:3

There are 13 results

Broad Topics > Trigonometry > Cosine

problem icon

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?

problem icon

Where Is the Dot?

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

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?

problem icon

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.

problem icon

Far Horizon

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

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

problem icon

Three by One

Stage: 5 Challenge Level: Challenge Level:1

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

problem icon

Cosines Rule

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

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.

problem icon

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?

problem icon

Pythagoras on a Sphere

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

Prove Pythagoras' Theorem for right-angled spherical triangles.

problem icon

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.

problem icon

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. . . .

problem icon

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?

problem icon

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.

problem icon

After Thought

Stage: 5 Challenge Level: Challenge Level:1

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


The NRICH Project aims to enrich the mathematical experiences of all learners. To support this aim, members of the NRICH team work in a wide range of capacities, including providing professional development for teachers wishing to embed rich mathematical tasks into everyday classroom practice. More information on many of our other activities can be found here.
Copyright © 1997 - 2012. University of Cambridge. All rights reserved.
NRICH is part of the family of activities in the Millennium Mathematics Project.