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Listed under:  Angles

### Angles are nice but are they cute?

Ever heard of acute angles? What about obtuse angles? Find out which is bigger than a right angle and which is smaller. See how to mark a right angle. And what's a straight angle?

### A cosy relationship between lines and angles

Which pairs of angles are the same when two lines intersect? What do you know about angles formed when a line intersects two parallel lines? Test your knowledge of geometric terms 'congruent', 'parallel', 'transversal' and 'corresponding', 'alternate' and 'co-interior' angles.

### Get your bearings using trig!

Apply your understanding of compass points (north, south, east and west) and trigonometry to solve problems about bearings and direction. Follow the steps of working out what the question is asking and drawing a labelled diagram. See how to go about solving the problem by using the correct trig ratio. In the second of these ...

### Elevated or depressed about trigonometry?

Learn how to solve the trigonometry problems in this video using sine, cosine and tangent. In order to solve problems with angles of depression, don't forget that alternate angles - when two parallel lines are crossed with a transversal - are equal. Now you're set!

### Trig 101: getting started!

Have you heard of trigonometry? See how to apply these labels to a right-angled triangle: angle, hypotenuse, adjacent and opposite. Find out about the three trig ratios for sine, cosine and tangent. Look out for a clever tip to remember these trig ratios! Now you are ready to apply that knowledge.

### Finding the missing side of a triangle

Know how to use trigonometry to find the unknown length of one side of a triangle? See how to do this with a right-angled triangle. All you need is an internal angle and the length of one side. Find out which trig ratio to use in three examples. Which one requires the use of cosine? Also look out for a clever tip to remember ...

### Finding the missing angle of a triangle

Do you know to use trigonometry to find the unknown angle of a triangle? See how to do this with a right-angled triangle. All you need is the length of two sides. Find out which trig ratio to use in these three examples. You'll notice that the inverse of sine, cosine and tangent will be used, so have your calculator at ...

### Solving problems using trig

Apply your knowledge of trigonometry to find the unknown length of one side of a triangle or one of its internal angles. Follow the steps used in two examples. First, work out what the question is asking, draw and label the right angled triangle with what you know, then use the correct trig ratio to solve the problem. One ...

### Trigonometry: finding angles

Look at an explanation of the trigonometric ratios: sine, cosine and tangent. Adjust the angles of a right-angled triangle within a unit circle (radius of one unit). Set the cosine, sine and tangent values of angles from 0–90 degrees. Identify the angle for each of the values. This learning object is one in a series of ...

### TIMES Module 22: Measurement and Geometry: introductory trigonometry - teacher guide

This is a 20-page guide for teachers containing an introduction to the three basic trigonometric ratios. A history of trigonometry concludes the module.

### EagleCat: trig-G

Explore the graphs of trigonometric equations in the form: (a) y = a sin[n(x - h)] + k, (b) y = a cos[n(x - h)] + k and (c) y = a tan[n(x - h)] + k. Use sliders or enter values to dilate, reflect and translate the basic trigonometric equations y = sin(x), y = cos(x) and y = tan(x), and observe the changes in the amplitude, ...

### Trigonometry: sine

Look at an explanation of the trigonometric ratios: sine, cosine and tangent. Adjust the angles of a right-angled triangle within a unit circle (radius of one unit). Find corresponding sides in similar triangles and find relationships between ratios. Identify the sine ratio and enter the sine values of angles from 0–90 ...

### Exploring relationships of angles

Explore angles formed by a transversal line intersecting parallel lines. Look at illustrations showing pairs of angles: vertically opposite, corresponding and alternate angles. Name pairs of angles to score points and help a monkey drive to the supermarket to buy food.

### Trig degrees

Use a unit circle tool to explore sine, cosine and tangent values in different quadrants. Determine the values for angles between 0° and 360°. Observe the symmetry and patterns of the functions to predict the behaviour of the graphs and the values for the functions in different quadrants. Observe the graphs animate and ...

### Trig degrees: tangent to 360

Use a unit circle tool to explore tangent values in different quadrants. Determine the tan Ø values for angles between 0° and 360°. Observe the symmetry and patterns of the functions to predict the behaviour of tan Ø in different quadrants. Observe the graph animate and visually connect it with the unit circle tool and ...

Use a unit circle tool to explore sine, cosine and tangent values in different quadrants. Determine the values for angles between 0 and 2π radians. Observe the symmetry and patterns of the functions to predict the behaviour of the graphs and the values for the functions in different quadrants. Observe the graphs animate ...

### Trigonometry: assessment

Test your understanding of angles and their sine, cosine and tangent values. Use a unit circle tool to find sine, cosine and tangent values in different quadrants. Use the tool to find the angle when given sine, cosine or tangent values. Determine the values for angles between 0° and 360°. Solve problems by using the unit ...

### TIMES Module 9: Measurement and Geometry: introduction to plane geometry - teacher guide

This is a 16-page guide for teachers. It provides an introduction to the initial ideas of plane geometry. Points and lines are introduced as fundamental objects in the study of geometry. Angles and parallelism are the initial areas of attention in a more formal approach to geometry that occurs from year 7.

### TIMES Module 26: Measurement and Geometry: circle geometry - teacher guide

This is a 44-page guide for teachers. It contains theorems on chords, arcs, angles and secants associated with circles.

### BBC Bitesize: intersecting and parallel lines - revision

These illustrated information sheets review the definition of intersecting and parallel lines, and angle facts for vertically opposite, alternate, corresponding and co-interior angles. A test that provides immediate feedback can be used for further consolidation. This resource is one of a series of online resources from ...