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Trigonometric Identities. sin2x+cosx=1 1+tan2x= secx. 1+cot2x= cscx. sinx=cos(90−x) =sin(180−x) cosx=sin(90−x) = −cos(180−x) tanx=cot(90−x) = −tan(180−x) Angle-sum and angle-difference formulas. sin(a± b) =sinacosb± cosasinb cos(a± b) =cosacosbmsinasinb tan( ) tan tan tan tan. a b a b a b. ± = ± 1m cot( ) cot cot cot cot.
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.
Trigonometry: Law of Sines, Law of Cosines, and Area of Triangles. Formulas, notes, examples, and practice test (with solutions) Topics include finding angles and sides, the “ambiguous case” of law of Sines, vectors, navigation, and more.
Determine whether the following functions are even, odd or neither. (a) sin2 x 2 cos2 x cos x (b) sin(cos x) (c) cos(sin x) (d) sin x + cos x. Points to Remember. 1. In general, a function is an even function if its graph is unchanged under re-ection about the y-axis.
Trigonometric Identities. Pythagoras’s theorem. sin2 + cos2 = 1 (1) 1 + cot2 = cosec2 (2) tan2 + 1 = sec2 (3) Note that (2) = (1)=sin2 and (3) = (1)=cos . Compound-angle formulae.
The sine, cosine and tangent of an angle are all defined in terms of trigonometry, but they can also be expressed as functions. In this unit we examine these functions and their graphs. We also see how to restrict the domain of each function in order to define an inverse function.
Trigonometric functions. The primary trigonometric functions are the sine and cosine of an angle. These are sometimes abbreviated sin(θ) and cos(θ), respectively, where θ is the angle, but the parentheses around the angle are often omitted, e.g., sin θ and cos θ.
