sin 2x = 2sin(x)cos(x) The sin 2x identity is a double angle identity. It can be used to derive other identities. Trig Identities Trigonometric identities,trig identitiesor trig formulas for short, are equations that express the relationship between specified trigonometric functions. They remain...
sin x cot x= 1 tan x Fundamental trig identity (cos x)2+(sin x)2=1 1+(tan x)2=(sec x)2 (cot x)2+1=(cosec x)2 Odd and even properties cos(−x)=cos(x)sin(−x)=−sin(x)tan(−x)=−tan(x)Double angle formulas sin(2x)=2sin x cos x cos(2x)=(cos x)2−...
Half-Angle Identity Formulas $$\cos\frac{\theta}{2}=\pm\sqrt{\frac{\cos\theta+1}{2}}\\ \sin\frac{\theta}{2}=\pm\sqrt{\frac{1-\cos\theta}{2}}\\ \tan\frac{\theta}{2}=\frac{1-\cos\theta}{\sin\theta}=\frac{1+\cos\theta}{\sin\theta} $$ These are the commonly used...
Sin X = 1 / 2orSin X = -1 The first equation gives two vales (X = 30o, X = 150o), the second equation gives one value (270o). Thus the solution of the original equation is: X = 30o, X = 150oand X = 270o. 2 Cos2X + Sin 2X = 0 Using the double angle identity, t...
2cos^2(θ) + sin(θ) = 1 cos^2(θ) + sin^2(θ) = 1, Pythagorean Identity cos^2(θ) = 1 – sin^2(θ) 2(1 – sin^2(θ)) + sin(θ) = 1 2– 2sin^2(θ) + sin(θ) = 1 2sin^2(θ) – sin(θ) – 1 = 0 (2sin(θ) + 1)(sin(θ) – 1) = 0 2s...
functions, because it's often unclear which identity or formula to use. For example, in the equation sin x cos x = 1/4, use the double angle formula cos 2x = 2 sin x cos x to substitute 1/2 cos 2x in the left side of the equation, yielding the equation 1/2 cos 2x = 1/4....
AnIdentityisNotaConditionalEquation Conditionalequationsaretrueonlyforsomevaluesofthevariable.Yousolveconditionalequationsby“balancingsteps,”suchasaddingthesamethingtobothsides,ortakingthesquarerootofbothsides.Weare“verifying”,not“solving”,identities,sowemustapproachidentitiesdifferently.2x21...
f f 1 x x for all x in the domain of f 1 f 1 f x x for all x in the domain of f. The interval where each inverse trigonometric function identity holds is given in the box on page 306. The identity sin Sin 1 x x suggests a way to think about the inverse trigono- metric ...
As Michael pointed out, this is based on a trig identity you should know. I recommend printing out a list of them to keep handy while you study (or bookmark the page in your textbook). The one in question is a sum formula: cos(x+y) = cos(x)cos(y) - sin(x)sin(y) You ha...
Multiply the numerator and denominator by the reciprocal of the bottom fractions to get