sin, cos, tan?

Question

Example:
Find the length of side x in the diagram below:





















The angle is 60 degrees. We are given the hypotenuse and need to find the adjacent side. This formula which connects these three is:
cos(angle) = adjacent / hypotenuse
therefore, cos60 = x / 13
therefore, x = 13 × cos60 = 6.5
therefore the length of side x is 6.5cm.



i dont understand this. =(

Answer 1

Maybe it's just me, but I can't see the diagram anyway. I'm assuming the triangle is a right-angled triangle. Anyway, the side which is adjacent is the side where the angle in question lies on. The opposite side is the side opposite to the angle in question, and the hypotenuse is always the longest side. So just remember SOHCAHTOA, sine = opp/hyp, cos = adj/hyp and tan = opp/adj. Sorry I couldn't help more :(

Answer 2

It would help if we could see the 'drawing' ☺
Just remember that the trig functions are ratios of the lengths of the sides in a right-angle triangle, **AND** that they are always the same for a given angle no matter how big or small the triangle may be. Once you know the length of the hypotenuse and that the angle formed between the hypotenuse and the adjacent side is 60°, you got it down.

cos(angle) = adjacent / hypotenuse (by definition)

cos(60) = x / 13 (so the hypotenuse is 13 units long and the angle it makes is 60°)

x = 13*cos(60°) (this is just simple algebra)

They left out that cos(60°) = 1/2. But you can get that off of your calculator.

x = 13*(1/2) = 6.5 (4'rd grade arithmetic)

One thing that you *have* to do is memorize the definitions. There is no magic in them, they are just definitions. But they are *useful* definitions that you need to remember so that you can work problems.

Why did some moron invent all of this trig stuff? It really wasn't to make your life difficult ☺ It all started about 3000 years ago in Egypt. Each year the Nile River would flood and wash topsoil down from the mountains. This was a good thing because the rest of Egypt was (and still is) hardpan desert that won't even support weeds. But after the floodwaters receded, there were only a couple of months to get crops planted before it became too late in the season tohave a prayer of getting them harvested before Winter set in. So all of that land had to be surveyed and measured out in a *hurry*. Worst of all, if you shorted one of the Pharos buddies a few hundred hectares of farmland, your head would probably end up on a pike. And that's where the basic ideas for trigonometry and trig tables were first developed. Like most math, it was invented to solve a real problem in the real world.

HTH ☺

Doug

Answer 3

See the source,

my advice is that you study the source link and understand "well" the triangle 30-60-90

and corresponding sine, and cosine of each angle.

to quote:

Example 1. Evaluate cos 60°.

Answer. For any problem involving a 30°-60°-90° triangle, the student should not use a table. The student should sketch the triangle and place the ratio numbers. 1:sqrt(3):2

Since the cosine is the ratio of the adjacent side to the hypotenuse, we see that cos 60° = ½.

yes, it is elementary - x=6.5, since cosine of 60 = 1/2


study the source it will guide you my padewan ;).

Answer 4

Sine Cosine and Tangent are just ratios of the lengths of two sides of the triangle, relative in position to the angle you are measuring.

Here's a good way to remember the formulas for each. Remember to draw a right triangle that includes the angles and sides you know. Once you do that, remember:

SOH CAH TOA

Sine = Opposite Side / Hypotenuse
Cosine = Adjacent Side / Hypotenuse
Tangent = Opposite Side / Adjacent Side

Then just start substituting values.

Answer 5

The main thing to keep in mind is that cos60 isn't a variable, it is a definite number (though I can't remember for the life of me what it would be, that's why we have calculators) so all you're really doing is taking cos60 (which you got from the information on the diagram) and multplying it by 13.

Answer 6

Sin = opp/hyp and tan = opp/adj.
Since you have adj and hyp, use cos.
Since the angle = 60,
cos 60 = x/13. Use calculator or table to get the value of cos 60 = 0.5

0.5 = x/13, mult by 13

x = 6.5

Answer 7

while coping with the sin, cos, tan, csc, sec, and cot, this is easiest to recollect in case you already know "sohcahtoa." you will see what "sohcahtoa" ability in a 2d. while coping with a triangle, this is maximum clever to discover the place theta is. depending on the place theta is on the triangle determines which trig function you employ. sin= opposite/hyponetuse cos= adjoining/hypotenuse tan= opposite/adjoining csc= hypotenuse/opposite sec= hypotenuse/adjoining cot= adjoining/opposite After looking theta, you will discover which component of the triangle is the hypotenuse, opposite component, and adjoining component. They hypotenuse is the longest component of the triangle (in appropriate triangles). opposite would be discovered immediately during (diagnally) from theta. adjoining would be discovered appropriate next to theta. wish this enables. :)