sin(x -y)=s in(x) cos(y) -cos(x)sin(y) cos(x -y) = cos(x) cos(y)+sin(x)sin(y) tan(x) -tan(y) tan(x -y)= 1 + tan(x) tan(y) LAW OF SINES sin(A) sin(B) sin(C) = = a b c. DOUBLE-ANGLE IDENTITIES sin(2x)=2s in(x) cos(x) cos(2x) = cos 2 (x) -sin 2 (x) = 2 cos 2 (x) 1 =1-2sin 2-(x) 2 tan(x) tan(2x)= 1 -tan 2 (x) HALF-ANGLE IDENTITIES r ⇣ ⌘x 1 cos For right-angled triangles, the ratio between any two sides is always the same and is given as the trigonometry ratios, cos, sin, and tan. Trigonometry can also help find some missing triangular information, e.g., the sine rule. The calculation is simply one side of a right angled triangle divided by another side we just have to know which sides, and that is where "sohcahtoa" helps. For a triangle with an angle θ , the functions are calculated this way: Example: what are the sine, cosine and tangent of 30° ? Laws of sines and cosines review. Google Classroom. Review the law of sines and the law of cosines, and use them to solve problems with any triangle. Law of sines. a sin ( α) = b sin ( β) = c sin ( γ) Law of cosines. c 2 = a 2 + b 2 − 2 a b cos ( γ) Want to learn more about the law of sines? Check out this video. Sine, Cosine and Tangent (often shortened to sin, cos and tan) are each a ratio of sides of a right angled triangle: For a given angle θ each ratio stays the same. no matter how big or small the triangle is. To calculate them: Divide the length of one side by another side. Example: What is the sine of 35°? Solution: In the triangle, the longest side (or) the side opposite to the right angle is the hypotenuse. The side opposite to θ is the opposite side or perpendicular. The side adjacent to θ is the adjacent side or base. Now we find sin ⁡θ, cos⁡ θ, and tan θ using the above formulas: sin θ = Opposite/Hypotenuse = 3/5. Plane Trigonometry. Spherical Trigonometry. In this article, let us discuss the six important trigonometric functions, ratios, trigonometry table, formulas and identities which helps to find the missing angles or sides of a right triangle. Trigonometry Ratios-Sine, Cosine, Tangent. Generalized trigonometry. Reference. Identities. Exact constants. Tables. Unit circle. Laws and theorems. Sines. Cosines. Tangents. Cotangents. Pythagorean theorem. Calculus. Trigonometric substitution. Integrals ( inverse functions) Derivatives. v. t. e. The main functions in trigonometry are Sine, Cosine and Tangent. They are simply one side of a right-angled triangle divided by another. For any angle " θ ": (Sine, Cosine and Tangent are often abbreviated to sin, cos and tan.) Sin is the ratio of the opposite side to the hypotenuse, cos is the ratio of the adjacent side to the hypotenuse, and tan is the ratio of the opposite side to the adjacent side. They are often written as sin(x), cos(x), and tan(x), where x is an angle in radians or degrees. Created by Sal Khan. KDrs66.