Trig integration
Integral of trig fuctions.
Result of calculation with derivative and integral is very often in form of those four functions.
trigonometric functions
inverse trigonometric funquantictions
hyperbolic functions
inverse hyperbolic functions
You must memorize the formulas first. There are 43. But because integration is just the backward process of differentiation, there are, in fact, only a score of equations to memorize. These functions themselves are already beyond our intuitional understanding. Each of us should personally invent a way to memorize them. Find find your own mnemonics. Without the slightest hesitation, memorise these 23 formulae first. Pythagoras figures can help you.
Trig functions on the unit circle or in coordinates system. Both are very useful, but if you refer to both simultaneously, that, in some cases, leads you to some confusion. On the unit circle, size of angle increases counterclockwise, but, in the coordinates system, it increases toward the right side.
And cosine value is horizontal on the unit circle but it is vertical in coordinates system. The unit circle is just only for the definition of each one of the trigonometric functions. The rest had better to be done with curve on coordinates system, especially when you are solving some geometric problems, even if they were problems with something in rotation. Very often you ought to forget the unit circle.
How about this kind of problem. In a big airport, a shuttle bus goes up and down between two terminals: South Terminal and North Terminal. The shuttle bus runs at a speed of sin t km/minute on the straight way of 2 km. As there is no passenger, the bus turns back without stopping at each terminal. First, the bus starts at South Terminal and goes up to North Terminal. Express its position observed from South Terminal. How long does it take to go back to South Terminel again? How is the acceleration?
When C = 1 , the curve is like this. The bus will be coming back in 2π minutes.
There are four more formulae for trigonometric functions.
Integration of tangent
Integral of cotangent
Integral of secant
Integral of cosecant
