Originally posted by Kelly_LSA'int that the truth.
Freshman never got beat up here at my school. That was just a rumor to scare them shitless. It's probably the same for your school.
Originally posted by Lucky BoyNah, advanced classes are easy as hell.
yeah i know what u mean cause those subjects are hard since their advanced.
Originally posted by Lucky BoyYeah, but there's a lot more to it.
oh okay.so trigonometry is studying triangles that seems easy.
Do u have to find area and volume of the shapes?
Lemme give you a quick overview:
Basic definitions
In this right triangle: sin(A) = a/c; cos(A) = b/c; tan(A) = a/b.
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In this right triangle: sin(A) = a/c; cos(A) = b/c; tan(A) = a/b.
The shape of a right triangle is completely determined, up to similarity, by the value of either of the other two angles. This means that once one of the other angles is known, the ratios of the various sides are always the same regardless of the size of the triangle. These ratios are traditionally described by the following trigonometric functions of the known angle:
* The sine function (sin), defined as the ratio of the leg opposite the angle to the hypotenuse.
* The cosine function (cos), defined as the ratio of the adjacent leg to the hypotenuse.
* The tangent function (tan), defined as the ratio of the opposite leg to the adjacent leg.
The adjacent leg is the side of the angle that is not the hypotenuse. The hypotenuse is the side opposite to the 90 degree angle in a right triangle; it is the longest side of the triangle.
\sin A = {\mbox{opp} \over \mbox{hyp}} \qquad \cos A = {\mbox{adj} \over \mbox{hyp}} \qquad \tan A = {\mbox{opp} \over \mbox{adj}} = {\sin A \over \cos A}
The reciprocals of these functions are named the cosecant (csc), secant (sec) and cotangent (cot), respectively. The inverse functions are called the arcsine, arccosine, etc. There are arithmetic relations between these functions, which are known as trigonometric identities.
With these functions one can answer virtually all questions about arbitrary triangles, by using the law of sines and the law of cosines. These laws can be used to compute the remaining angles and sides of any triangle as soon as two sides and an angle or two angles and a side or three sides are known. These laws are useful in all branches of geometry since every polygon may be described as a finite combination of triangles.
[edit] Extending the definitions
Graphs of the functions sin(x) and cos(x), where the angle x is measured in radians.
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Graphs of the functions sin(x) and cos(x), where the angle x is measured in radians.
The above definitions apply to angles between 0 and 90 degrees (0 and π/2 radians) only. Using the unit circle, one may extend them to all positive and negative arguments (see trigonometric function). The trigonometric functions are periodic, with a period of 360 degrees or 2π radians. That means their values repeat at those intervals.
The trigonometric functions can be defined in other ways besides the geometrical definitions above, using tools from calculus or infinite series. With these definitions the trigonometric functions can be defined for complex numbers. The complex function cis is particularly useful
\mathrm {cis} (x) = \cos x + i\sin x \! = e^{ix}
See Euler's formula.
[edit] Mnemonics
The sine, cosine and tangent ratios in right triangles can be remembered by SOH CAH TOA (sine-opposite-hypotenuse cosine-adjacent-hypotenuse tangent-opposite-adjacent). It is commonly referred to as "Sohcahtoa" by some American mathematics teachers, who liken it to a (nonexistent) Native American girl's name. See trigonometry mnemonics for other memory aids.
[edit] Calculating trigonometric functions
Main article: Generating trigonometric tables
Trigonometric functions were among the earliest uses for mathematical tables. Such tables were incorporated into mathematics textbooks and students were taught to look up values and how to interpolate between the values listed to get higher accuracy. Slide rules had special scales for trigonometric functions.
Today scientific calculators have buttons for calculating the main trigonometric functions (sin, cos, tan and sometimes cis) and their inverses. Most allow a choice of angle measurement methods, degrees, radians and, sometimes, grad. Most computer programming languages provide function libraries that include the trigonometric functions.