Trigonometry

Volume= 0.5(area of the base)(distance between 2 faces)

Volume of a triangular prism = (area of the base) (perpendicular distance between the 2 bases of the prism)

Since it is a triangular prism, the base of the prism is triangle in shape.

Let b be the base of the triangle and h be the height of the triangle.

Area of the triangle = 1/2 b*h or b*h/2.

Let the Perpendicular distance between the two bases of the prism be l units.

Then the volume of the triangular prism = (1/2)*b*h*l

Volume = 1/2*b*h*l cubic units.

So basically the formula is base times height then divided by two. (Only for the triangle.)

For example, if one triangle's height is 6 and height is 11, then it would be like this:

6 x 11= 66, divided by two = 33.

The absolute basics to trigonometry.

You will need a calculator for this, unless you want to do it the old and amazingly accurate (for it's time) trig tables that used to be used (if you can find one)

First you have to understand that basic trigonometry does not cover any more than right angled triangles

Secondly, the names of the sides of a triangle. The side opposite to the right angle is known as the hypotenuse (will abbreviate to hyp). The side opposite to the angle that you wish to find or the known angle (DO NOT USE THE RIGHT ANGLE AS AN ANGLE) is known as the opposite side (opp). The other side is known as the adjacent (adj) (if your triangle has more than three sides there is a problem).

generally the angle that you wish to find will be known as theta

the basic rules to trigonometry can be summarized in one easy to remember word

SOHCAHTOA more easily understood as SOH|CAH|TOA

(the equation that you use is dependent on the the sides available and what information is given a the beginning of the problem)

SOH means that Sine(theta) = Opp/Hyp

CAH means that Cos(theta) = Adj/Hyp

TOA means that Tan(theta) = Opp/Adj

The angle theta can also be calculated by using the formulas

Theta = sin-1(opp/hyp)

Theta = cos-1(adj/hyp)

Theta = tan-1(opp/adj)

where the -1 means that the trigonometric function simply is applied to the whole other side of the equation and does not affect the side that was not originally on

Note: anything in brackets after a sin, cos or tan is part of that sin, cos or tan. It cannot be separated unless you apply the inverse (-1 ) to the other side and remove it from it's original side

Another note: Sin is pronounced Sine (like swine without the 'w') all the maths teachers that I know hate it when it is pronounced Sin.

Finally: Trig is not that hard, all that hard work was done when it was made (and even when past generation had to trawl through tables to find the right (approximate to maybe three decimals) number. All that you really need is to know basic algebra, how to use a scientific calculator, and SOHCAHTOA.

Differentiating is the act of finding the derivative of a function, thus allowing you to find out how the function changes as its input changes, such as finding the rate of change of the gradient of the function, and when differentiating with respect to time can allow you to give equations explaining the motion of various objects, depending on how you differentiate the functions. There are two main types of differentiation, ordinary differentiation and partial differentiation, the rules outlined below are for ordinary differentiation. While the rules for partial differentiation are not that dissimilar, they do not need to be known outside of university level mathematics and physics.

(using f' and g' to denote the derivative of the functions f and g of x respectively, x is a variable, o indicates a composite function, all other letters are constants, rules in bold are important)

f = xn, f' = nx(n-1) elementary power rule

f = a, f' = 0 constant rule

f = ax, f' = a derivative of a linear function is a constant

(af +bg)' = af'+bg' linearity of differentiation, leading to the 3 following,

(af)' = af' constant multiple rule

(f+g)' = f'+g' sum rule

(f-g)' = f'-g' subtraction rule,

(fg)' = f'g + fg' product rule

(fog)' = (f(g))' = (f'(g))g' = (f'og)g' chain rule

f = 1/g, f' = -g'/g2 reciprocal rule

(f/g)' = (f'g-fg')/g2 quotient rule

f=sin(x), f'=cos(x)

f=cos(x), f'=-sin(x)

f=tan(x), f'=sec2(x)

f=sec(x), f'=sec(x)tan(x)

f=cosec(x) f'=-cosec(x)cot(x)

f=cot(x), f'=-cosec2(x)

f=exp(ax), f'=a*exp(ax)

f=exp(axn), f'=anx(n-1)*exp(axn)

f=ax, f'=(log(a))*ax

f=log(x), f'=1/x

f=log(xn), f'=nx(n-1)/xn

f=xx, f'=xx(1+log(x))

these are just the simple rules of differentiation for various functions, there are a LOT more, but they are generally only of use at university levels.