## Posts tagged with sine

### Trig Ratios Unplugged

Sine, Cosine and Tangent are the three main trigonometric or Trig Ratios. Before we look at these in more detail, where did these strange terms come from? Trigonometric functions were studied by Hipparchus of Nicaea (180–125 BC), Ptolemy of Egypt (90–165 AD), Aryabhata (476–550), Varahamihira, Brahmagupta, Ulugh Beg and others (14th century). The word “sine” […]

### Riding the Sine Wave…

A sine wave is a repetitive change or motion which, when plotted as a graph, has the same shape as the sine function. For example, on the right is a weight suspended by a spring. As it bounces up and down, its motion, when graphed over time, is a sine wave. In reality, friction and […]

### Sound Waves and Noise Cancelling

Play the note A Play the (shifted) note A You may have seen advertisements for “noise reducing” headphones. Here’s a rough idea of how they work. First they figure out what kind of noise is reaching your ears. Essentially this means it figures out the sine waves of the ambient sounds. Then it creates additional […]

### Sine Method used to measure tallest tree

Scientists recently measured the tallest tree in New Zealand at just over 81 metres. How did they do this? Using lasers and the Sine method – that is, the Sine of the angle formed by the lasers gave the height/hypotenuse. Read more here. (Note: This image is not of the tallest tree but gives some […]

### Trig Ratios – Part 2

Look at the following equations and see if you can find the mathematical pattern; Sin 30 = 0.5 Cos 60 = 0.5 Sin 60 = 0.866 Cos 30 = 0.866 Sin 0 = 0 Cos 90 = 0 Sin 45 = 0.707 Cos 45 = 0.707 Sin 80 = 0.985 Cos 10 = 0.985 […]

### Hear Ye, Hear Ye, Math = Sound Waves!

There is a lot of information on the web about sound waves and the mathematical patterns surrounding them. For example, the changes in air pressure produce sine curves such as this one below. Of course, there are complex formulae that apply in calculating sound effects. When we listen to a radio or TV we hear […]