Trigonometric Identities - Miami
sin x y 2 The Law of Sines sinA a = sinB b = sinC c Suppose you are given two sides, a;band the angle Aopposite the side A The height of the triangle is h= bsinA Then
DOUBLE-ANGLE, POWER-REDUCING, AND HALF-ANGLE FORMULAS
x + sin 2x = 1 + sin 2x 1 + sin 2x = 1 + sin 2x (Pythagorean identity) Therefore, 1+ sin 2x = 1 + sin 2x, is verifiable Half-Angle Identities The alternative form of double-angle identities are the half-angle identities Sine • To achieve the identity for sine, we start by using a double-angle identity for cosine cos 2x = 1 – 2 sin2
Formulas from Trigonometry
Formulas from Trigonometry: sin 2A+cos A= 1 sin(A B) = sinAcosB cosAsinB cos(A B) = cosAcosB tansinAsinB tan(A B) = A tanB 1 tanAtanB sin2A= 2sinAcosA cos2A= cos2 A sin2 A tan2A= 2tanA
Formule trigonometrice a b a b c b a c - Math
1 sin = a c; cos = b c; tg = a b; ctg = b a; (a; b- catetele, c- ipotenuza triunghiului dreptunghic, - unghiul, opus catetei a) 2 tg = sin cos ; ctg = cos sin : 3 tg ctg = 1: 4 sin ˇ 2 = cos ; sin(ˇ ) = sin : 5 cos ˇ 2 = sin ; cos(ˇ ) = cos : 6 tg ˇ 2 = ctg ; ctg ˇ 2 = tg : 7 sec ˇ 2 = cosec ; cosec ˇ 2 = sec : 8 sin 2 + cos
Euler’s Formula and Trigonometry
3 Euler’s formula The central mathematical fact that we are interested in here is generally called \Euler’s formula", and written ei = cos + isin Using equations 2 the real and imaginary parts of this formula are cos = 1 2 (ei + e i ) sin = 1 2i (ei e i ) (which, if you are familiar with hyperbolic functions, explains the name of the
Integral Calculus Formula Sheet
Integral Calculus Formula Sheet Derivative Rules: 0 d c dx nn 1 d xnx dx sin cos d x x dx sec sec tan d x xx dx tan sec2 d x x dx cos sin d x x dx csc csc cot d x xx dx cot csc2 d x x dx d aaaxxln dx d eex x dx dd cf x c f x dx dx
85 Integrals of Trigonometric Functions
1 2cos(2x)+cos2(2x) i dx = 1 4 x sin(2x)+ x 2 + 1 8 sin(4x) +C = 3 8 x 1 4 sin(2x)+ 1 32 sin(4x)+C using the formula for R cos2(2u)du J Practice 1 Evaluate Z cos4(x)dx For odd powers of sine or cosine we can split off one factor of sine or cosine and rewrite the remaining even power using the identities sin2(q) = 1 2cos2(q) or cos (q) = 1
Trig Cheat Sheet - Lamar University
sin hypotenuse q= hypotenuse csc opposite q= adjacent cos hypotenuse q= hypotenuse sec adjacent q= opposite tan adjacent q= adjacent cot opposite q= Unit circle definition For this definition q is any angle sin 1 y q==y 1 csc y q= cos 1 x q==x 1 sec x q= tan y x q= cot x y q= Facts and Properties Domain The domain is all the values of q that