I Used to Know That_ Stuff You Forgot From School - Caroline Taggart [23]
This can also be remembered using the formula a2 + b2 = c2, where c is the hypotenuse.
The burning question, of course, is, Why does it matter? Well, it could have had some practical value in the ancient world. It has been suggested, for example, that the Egyptians could have used ropes in the proportion 3:4:5 to produce right angles when building the pyramids. Unfortunately, there isn’t the remotest scrap of evidence that they did any such thing. In fact, the Pythagorean theorem matters most to mathematicians because it is fundamental to our next topic.
Trigonometry
Trigonometry is “the branch of mathematics that deals with the relations between the sides and angles of a triangle,” and a trigonometric function is “any function of an angle that is defined by the relationship between the sides and angles of a right-angled triangle.”
There are six basic trigonometric functions: sine, cosine, tangent, cotangent, secant, and cosecant, and they are calculated as follows. In a right-angled triangle where the other two angles are valued at x and y degrees, the side opposite x is a, the side opposite y is b, and the hypotenuse is c:
sin x = a/c
cos x = b/c
tan x = a/b
cot x = b/a
sec x = c/b
cosec x = c/a
Why do we care? Well, the point is that the functions or ratios remain the same whatever the size of the triangle. So if you know the sine of a 90° angle in a triangle whose sides measure 3, 4, and 5 inches, you can extrapolate all sorts of measurements for a much larger triangle with the same proportions.
The trigonometric version of the Pythagorean theorem tells us that for any angle x,
sin2x + cos2x = 1,
where sin2x is a conventional way of writing (sin x)2 without the need for brackets. If you know the sine of an angle, you can use this formula to calculate all the rest of the trigonometric functions given above.
Trigonometry is vital to the study of higher mathematics and the sciences. At a more comprehensible and practical level, it is used in land surveying, mapmaking, engineering, astronomy, geography, satellite navigation systems, and so on.
SCIENCE
The world of science is so vast and expanding that to condense it into 30 pages seems like a futile experiment. Every school system teaches the topic differently, so what may seem familiar and commonplace to one person can remain a mystery to others. Consider this chapter the foundation on which you can build.
Biology
The term biology comes from the Greek, meaning study of life; therefore, this field of learning concerns plants and animals and how the human body works.
☞ PHOTOSYNTHESIS
This is the process by which plants convert carbon dioxide and water into the carbohydrates they need for growth, using energy that they absorb from light (hence, the photo element). Light is absorbed into the plant by the green pigment called chlorophyll, stored mainly in the leaves, which provides the green color of so many plants. In fact, plants need only the hydrogen element from water (H2O), so photosynthesis releases oxygen back into the atmosphere, enabling the rest of us to breathe.
☞ THE STRUCTURE OF A PLANT
The flower contains the plant’s reproductive organs. The stigma, style, and ovary make up the carpel, which contains the female cells; if a flower has more than one carpel, these combine to form the pistil. The male organ is called the stamen and consists of an anther that contains the pollen sacs and is supported on a filament. Most plants self-pollinate, but some, such as certain hollies and the kiwifruit, require a male and female plant of the same species in order to reproduce.
The leaves enable the plant to feed and breathe. They contain the chlorophyll that is essential to photosynthesis, which absorbs light. Leaves also contain pores (stoma), through which gases and water are absorbed and released back into the atmosphere. The shape of the leaf reflects the plant’s needs: big, broad leaves are designed to absorb