how are tan sin and cos determined in math....explain in compete detail from top to bottom?

Question

i want to know why you get any answer from typing sin 36 in a calculator.....what process does the calculator use to deviate the answer

Answer 1

Sine (sin), cosine (cos), and tangent (tan) are three of the six trigonometric functions--they are basic definitions involved in trigonometry. While trigonometry applies to all triangles and even some circular functions, the basic defintions are founded upon right triangles.

Each of the trigonometric functions calculates the ratio between two sides of a triangle containing the angle that you are working with. The definitions are:
sine (sin) = opposite/hypotenuse
cosine (cos) = adjacent/hypotenuse
tangent (tan) = opposite/adjacent
cotangent (cot) = adjacent/opposite
secant (sec) = hypotenuse/adjacent
cosecant (csc) = hypotenuse/opposite

We only have three of these on the calculator, because the others are reciprocals. That is sin = 1/csc, cos = 1/sec, and tan = 1/cot. So when we need the cot, sec, or csc, we can use the reciprocal function to find the value.

So if you enter "sin 36" in the calculator, you are finding out the ratio between the opposite leg and the hypotenuse when you have a 36 degree angle in a right triangle. Since triangles with the same angle measures are similar--the ratios between the legs stay the same no matter how large or small the triangle becomes--these ratios always stay the same.

Answer 2

Hi, sin is soh, cos is cah, tan is toa
S=opposite/hypotenuse C= adjacent/hypotenuse T= Opposite/adjacent.

(You have a triangle with 3 sides. The longest side is the hypotenuse
The side opposite that is the opposite side, the 3rd remaining side is the adjacent side).

When you type in sin 36, 36 is the angle you want to find the sin of so it does the side opposite the 36 degree angle divided by the hypotenuse-longest side of the triangle.

Answer 3

they're abbreviations for the "sine", "cosine" and "tangent" of an attitude. they're the three straightforward applications of trigonometry. enable's say you've a wheelchair ramp that makes an attitude of x degrees from the floor. imagine of the facet view of the ramp as a accurate triangle. you've the attitude (x) it makes with the floor, and three aspects: the facet opposite of that attitude (that is the height of the ramp), the facet adjoining to that attitude (that is the dimensions of ramp alongside the floor) and the triangle's hypotenuse (that is the full facet, which runs diagonally and the wheelchair runs on). The sine, cosine, and tangent for an attitude "x" are defined as follows: sin(x) = opposite / hypotenuse cos(x) = adjoining / hypotenuse tan(x) = opposite / adjoining So enable's say the ramp made an attitude of 30 degrees with the floor. you'll discover that no count how short or lengthy the ramp is, that sin(30) continually equals a million/2, and cos(30) continually equals ?3 / 2, and tan(30) continually equals ?3 / 3. those applications are helpful because they teach up in an excellent style of diverse formula.

Answer 4

There is an easy mnemonic device: SOH-CAH-TOA (say it out loud and remember it.

The Sine of any angle is the Opposite divided by the Hypotenuse (SOH)
the Cosine is the Adjacent divided by the Hypotenuse (CAH)
The Tangent is the Opposite divided by the Adjacent (TOA)

Answer 5

Open your math book!

Answer 6

google away