explain trigonometry in simple steps?

Question

cause i cant seem to understand the methods on other sites

Answer 1

Let ABC be a right-angled triangle with the right angle at C.
The side AB opposite the right angle is called the hypotenuse. This is always the longest side.

Referring to angle A, the opposite side is BC, and the remaining side AC is the adjacent side.
The ratios sine, cosine and tangent are defined as ratios of the three sides.

The mnemonic SOH CAH TOA tells you that:
sin(A) is opposite over hypotenuse (BC/AB);
cos(A) is adjacent over hypotenuse (AC/AB);
tan(A) is opposite over adjacent (BC/ AC).

The ratios for angle B are obtained in the same way, but because AC is the side opposite angle B, that means the adjacent side is BC.
sin(B) is opposite over hypotenuse (AC/AB);
cos(B) is adjacent over hypotenuse (BC/AB);
tan(B) is opposite over adjacent (AC/ BC).

If you know AC and angle B, for example, and want to find AC, then think 'What equation can I write down to give AC?'
AC is opposite B, and you want AB which is the hypotenuse. The ratio is therefore sine. From the definition above:
AC / AB = sin(B).
Take reciprocals of each side to get AB:
AB / AC = 1 / sin(B)
Multiply by AC:
AB = AC / sin(B).

Answer 2

Explain Trigonometry

Answer 3

Suppose a builder has to make a ramp so that wheelchairs users can get into a building.The builder might be told that the slope to the horizontal should be (say) 5 degrees.It would not be practical to use a protractor so instead one of the (ancient) trigonometric fractions(or ratios) would be used.Suppose the 'chair has to rise 1m. at not more than 5 deg.builder has to calculate how far away from the entrance the slope must start.In this case we are only wanting to find the length of the side(the base)which is at right angle to the side whose height has to be 1 m.So we use the tangent ratio.
we get height/base =tan of 5 degrees
1/base=0.087
1=0.087Xbase
base =1/.087
base =11.5 metres(or say12 metres)

So now the builder knows that a slope slighly shallower than 5 deg.is equal to a rise of 1:12.
Without drawings it is difficult to simplify this,but if you really want to understand this use some squared paper to make a scale drawing of a ramp rising 1unit over a horizontal run of 12 units.Then try drawing a slope of 1:8 ;calculate the
tangent (convert 1/8 to the decimal fraction 0.125 using a calculator) then press shift tan and read of the angle in deg.
see if your calculation agrees with what you measure it as with a protractor.Try some other examples to get confident.
Your calculator converts angles measured in degrees(fraction of a full turn) into angles measured as the ratio of lengths of given sides;and back.

Answer 4

The branch of mathematics concerned with specific functions of angles and their application to calculations.

There are six functions of an angle commonly used in trigonometry.
Their names and abbreviations are sine (sin), cosine (cos), tangent (tan), cotangent (cot), secant (sec), and cosecant (csc).
These six trigonometric functions in relation to a right triangle are displayed in the figure. (click on link)

For example, the triangle contains an angle A, and the ratio of the side opposite to A and the side opposite to the right angle (hypotenuse) is called the sine of A, or sin A;

The other trigonometry functions are defined similarly. These functions are properties of the angle A independent of the size of the triangle, and calculated values were tabulated for many angles before computers made trigonometry tables obsolete.

Trigonometric functions are used in obtaining unknown angles and distances from known or measured angles in more complicated geometric figures.

These calculations make use of a collection of Advanced rules i.e. Cosine Rule and Sine Rule etc.

Answer 5

Trigonometry is about triangles. Triangles have 3 sides and, in a plane, the 3 angles add to 180°.
.

Answer 6

I understand it as follows:
its all about triangles and primarily finding the size of right angled triangles.
there are certain ratios that can be used to find out the size of angles if you are given certain lengths of sides.
So, if you know the length of the side adjacent to the angle and the hypothenuese then use use a special ratio called cos; if you know the length of the opposite angle and hypotenuse then you use the ratio called sine, if you know the length of the opposite and adjacent then you use tan.

the way to remember it is

SOH CAH TOA.

for sin you divide the length of the opposite /hypotenuese on your calculator, you will get a decimal number, you press your sin key (of shift sin-1) and the calculator multiplies this decimal number with the sin ratio. You will then get the size of the angle.


Best thing to do is to do lots of practise - I would recommend the BBC GCSE website
hope this helps.

Answer 7

SOH CAH TOA

SOH=Sin(sine). Opposite over hypotenuse.
CAH=Cos(Cosine). Adjacent over hypotenuse.
TAO=Tan(Tangent). Adjacent over opposite.

To remember these formulas are easier to remember if you put them in the form of triangles. A few weeks ago, i had a maths exam and the teacher had not taught us trigonometry. We had 2 50-minute lessons but i managed to learn it and get the top grade in my exam. You will too. x

Answer 8

SOH, CAH, TOA. Simple. If you don't get it don't worry, I learnt about it over thirty years ago and I never had any use for it. Read a trashy novel or listen to some good music instead!

Answer 9

csc 5π/4 = 1/sin5π/4 = 1/( -√2/2) = 1 / (-√2/√2√2) => 2 = √2√2 = 1/ (-1/√2) = -√2

Answer 10

Maybe you aren't drawing the triangles.