sin 2x + cos x = 0 (substitute 2sin x cos x for sin 2x)2sin x cos x + cos x = 0 (divide by cos x each term to both sides)2sin x + 1 = 0 (subtract 1 to both sides)2sin x = -1 (divide by 2 to both sides)sin x = -1/2Because the period of the sine function is 360⁰, first find all solutions in [0, 360⁰].Because sin 30⁰ = 1/2 , the solutions of sin x = -1/2 in [0, 360] arex = 180⁰ + 30⁰ = 210⁰ (the sine is negative in the third quadrant)x = 360⁰ - 30⁰ = 330⁰ (the sine is negative in the fourth quadrant)Thus, the solutions of the equation are given byx = 210⁰ + 360⁰n and x = 330⁰ + 360⁰n, where n is any integer.
YES!!!! Sin(2x) = Sin(x+x') Sin(x+x') = SinxCosx' + CosxSinx' I have put a 'dash' on an 'x' only to show its position in the identity. Both x & x' carry the same value. Hence SinxCosx' + CosxSinx' = Sinx Cos x + Sinx'Cosx => 2SinxCosx
All others can be derived from these and a little calculus: sin2x+cos2x=1 sec2x-tan2x=1 sin(a+b)=sin(a)cos(b)+sin(b)sin(a) cos(a+b)=cos(a)cos(b)-sin(a)sin(b) eix=cos(x)+i*sin(x)
28 The Law of Sines: a/sin A = b/sin B = c/sin C 24/sin 42˚ = c/sin (180˚ - 42˚ - 87˚) since there are 180˚ in a triangle. 24/sin 42˚ = c/sin 51˚ c = 24(sin 51˚)/sin 42˚ ≈ 28
sin(30) = sin(90 - 60) = sin(90)*cos(60) - cos(90)*sin(60) = 1*cos(60) - 0*sin(60) = cos(60).
Sin -30
-0.5
SQRT(3)/4 - 1/4
Not certain but calculator says 0.577, may have something to do with circle quadrants ie 210 is 30 degrees into third quadrant of circle (tan 30 = 0.577) see google - tan in circle, then scroll to sin, cos, tan
210
44,100. Typing in "210*210" in google will give you the answer.
7% of 210 = 14.7 = 7% * 210 = 7%/100% * 210 = 0.07 * 210 = 14.7
210 = 1 x 210 210 = 2 x 105 210 = 3 x 70 210 = 5 x 42 210 = 6 x 35 210 = 7 x 30 210 = 10 x 21 210 = 14 x 15
4% of 210 = 4% * 210 = 0.04 * 210 = 8.4
45% of 210= 45% * 210= 0.45 * 210= 94.5
81% of 210= 81% * 210= 0.81 * 210= 170.1
5% of 210 = 5% * 210 = 0.05 * 210 = 10.5