What is a differential equation, the pendulum equation, and some basic numerical methods

The introduction to a series on visualizing core ideas of linear algebra.

The introduction to a series on visualizing core ideas of linear algebra.

New ReviewWhen learning about sine and cosine it can be tricky to remember what they mean and how they are useful. In this video I hope to show you exactly what you need to know.

New ReviewIn this video I am going to work through how to evaluate a basic trig function using the unit circle and one more difficult

Pupil outcome: I can use my knowledge of right-angled trigonometry to solve problems. Key learning points: - Sometimes an answer may be best left in an exact form - When dealing with right-angled trigonometry, it is important to look at...

Pupil outcome: I can apply trigonometric ratios to practical situations including angles of elevation and depression. Key learning points: - Trigonometric ratios are used in many scenarios - Trigonometric ratios are used to calculate the...

Pupil outcome: I can read values from the graphs and can identify how many solutions exist within a given range. Key learning points: - Reading solutions from trigonometric graphs is the same as reading solutions from any other graph -...

Pupil outcome: I can calculate trigonometric ratios for 30° and 60°. Key learning points: - The trigonometric ratios for 30° and 60° can be calculated using an equilateral triangle - The triangle should have lengths of 2 units - By...

Pupil outcome: I can use my knowledge of right-angled trigonometry to solve problems. Key learning points: - Sometimes an answer may be best left in an exact form - When dealing with right-angled trigonometry, it is important to look at...

Pupil outcome: I can use my knowledge of trigonometry to solve problems. Key learning points: - Non right-angled trigonometry can be applied in various contexts - It has the potential to be applied whenever a triangle can be drawn

Pupil outcome: I can appreciate the range of values of the trigonometric functions. Key learning points: - The unit circle is a circle with a radius of one - The unit circle is centered on the origin - The sine of an angle is the...

Pupil outcome: I can calculate trigonometric ratios for 0°, 45° and 90°. Key learning points: - The trigonometric ratios for 45° can be calculated using a square - The square should have lengths of 1 unit - By splitting the square into...

Pupil outcome: I can draw the graphs for the trigonometric functions sine and cosine. Key learning points: - The unit circle can help you predict what the graphs of the trigonometric functions will look like - The sine and cosine graphs...

Pupil outcome: I can use the formula for the area of any triangle. Key learning points: - The formula for the area of any triangle can be used if the lengths of 2 sides are known - The size of the angle between the two sides must also be...

Pupil outcome: I can use the sine ratio to find the missing side or angle in a right-angled triangle. Key learning points: - The sine ratio involves the hypotenuse, opposite and the angle - If you know the length of the hypotenuse and...

Pupil outcome: I can derive the formula for the area of any triangle. Key learning points: - The formula for the area of a right-angled triangle is 0.5 x base x perpendicular height - With an equilateral or isosceles triangle, you can...

Pupil outcome: I can use the sine ratio to find the missing side or angle in a right-angled triangle. Key learning points: - The sine ratio involves the hypotenuse, opposite and the angle. - If you know the length of the hypotenuse and...

Pupil outcome: I can see how the trigonometric functions are derived from measurements within a unit circle and how this can be utilised. Key learning points: - Trigonometric functions are derived from measurements within a unit circle -...

Pupil outcome: I can appreciate that the trigonometric functions are derived from measurements within a unit circle. Key learning points: - The unit circle is a circle with a radius of one. - The unit circle is centered on the origin. -...

How do you graph secant and cosecant? And, how do these graphs compare to the graphs of sin(x) and cos(x)? In this video, we answer these questions by deriving the graphs for secant and cosecant, and then identifying the domain, range,...

How do I graph sin and cos? In this video, we use the unit circle to derive the graphs for sine and cosine. These periodic functions are very similar, but there are some slight differences.

What are the trigonometric functions and how did the sine function allow Indian astronomers to prove that the Sun was 400 times farther from Earth than the Moon? Maths - Shape A Twig Math Film. Reinforce and extend the learning required...

Hear sine waves as sound, and discover the equations that describe them: and the effect of increasing or decreasing the variables of amplitude and frequency. Maths - Shape A Twig Math Film. Reinforce and extend the learning required by...