Chapter 6 - Trigonometry |
| Trigonometry - Trigonometric Laws - Contents |
Due to the nature of the functions of trigonometry certain laws can be applied. The trigonometric laws of identity include these important reciprocal equalities. The tangent is the sine divided by the cosine. The cotangent is equal to one over the tangent, or the cosine divided by the sine. The secant is equal to one over the cosine and the cosecant is equal to one over the sine. In the unit circle the cosine squared plus the sine squared of an angle is equal to one. This last identity law is derived from the Pythagorean Theorem. The trigonometric laws of sines and cosines can be used to solve a triangle which is finding all three angles and three sides of any triangle given three out of the six. The law of sines states that in any triangle, not just a right triangle, the ratio of the sine of each angle to its opposing side is the equivalent for all three angles. The trigonometric law of sines can be used to solve any triangle given two angles and an opposite side, or two sides and an opposite angle. The law of cosines states that in any triangle the square of one side is equal to the sum of the squares of the other two sides, minus the multiplied product of two times the other two sides times the cosine of the opposing angle to the first side. The trigonometric law of cosines can be used to solve a triangle given all three sides, or two sides and the included angle. From these laws and the fact that the geometric area of any triangle is one-half the base times the height, the area can be also be shown to be equal to one-half times any two sides times the sine of the included angle.
| Trigonometry - Trigonometric Laws - Definitions |
Laws for any triangle:
A triangle with side a opposite angle theta-1,
side b opposite angle theta-2
and side c opposite angle theta-3
follows these laws.Law of sines:
Sine (theta-1) / a = Sine (theta-2) / b = Sine (theta-3) / c.Law of cosines:
a² = b² + c² - (2 x b x c x Cosine (theta-1)).
| Trigonometry - Sections - Chapters | ||
| 1 - Pythagorean Theorem | 2 - Theorem Proof | 3 - Pi Value |
| 4 - Trigonometry Conventions | 5 - Sine Function | 6 - Cosine Function |
| 7 - Tangent Functions | 8 - Trigonometry Laws | |
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