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Basic Identities. The functions cos(θ) and sin(θ) are defined to be the x and y coordinates of the point at an angle of θ on the unit circle. Therefore, sin(−θ) = − sin(θ), cos(−θ) = cos(θ), and sin2(θ) + cos2(θ) = 1. The other trigonometric functions are defined in terms of sine and cosine: tan(θ) = sin(θ)/ cos(θ) cot(θ ...
Fundamental trig identity. cos(. (cos x)2 + (sin x)2 = 1. 1 + (tan x)2 = (sec x)2 (cot x)2 + 1 = (cosec x)2.
Pythagorean Identities. 2 2 sin θ + cos θ = 1. 2 + tan θ = 2 sec θ. 1 + cot 2 θ = csc θ.
1 Sine and Cosine Rules. In the triangle ABC, the side opposite angle A has length a, the side opposite angle B has length b and the side opposite angle C has length c. The sine rule states. A. sin A sin B sin C. = = b c. C. a.
For example, Sin(40) can be expressed as the double angle Sin2(20) Why would you use them? Sometimes double angles equations and make it 2 Sin (90) Sin (180) 2 easier to perform complex operations. Double Angle Formulas: Sin 2X = Sin2X = Sin(X + X) Examples: Sin 2(90) Sin 2(90) Sin 2(30) Sin 2(30) (U sing Sum Identity) SinXCosX + CosXSinX 2SinXCosX
ność między kątami: ˇ= + 2. Możemy więc obliczyć wartość sin w trójkącie prostokątnym , tzn. sin = pjxj x2+y2. Następnie z własności wartości bezwzględnej i definicji funkcji trygonome-trycznych dowolnego kąta dostajemy: sin = jxj p x2 + y2 = x x2 + y2 = cos 7
Important Trigonometric Formulas. Textbook of Algebra and Trigonometry for Class XI. Available online @ http://www.mathcity.org, Version: 2.0. sin 2 + cos 2 = 1 1 + tan 2 = sec. 2 1 + cot 2 = csc. sin( − ) = − sin cos( − ) = cos tan( − ) = − tan .
