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sin2x-cosx=0? | Yahoo Answers

source : yahoo.com

sin2x-cosx=0? | Yahoo Answers

sin 2x – cos x = 0

We need to use the sine double angle trig identity that sin(2x) = 2 cos(x) sin(x). So…

2 sinx cosx – cosx = 0

==> factor

cosx (2sinx – 1) = 0

So, we have two equations:

cos x = 0 *AND* (2sinx – 1) = 0

First, cos x = 0

==> x = π/2, 3π/2, 5π/2…

Next, 2 sinx – 1 = 0

2 sinx = 1

sinx = 1/2

==> x = π/6, 5π/6, 13π/6…

So, we need to put our answers in terms of any integer ‘n,’ so we have three sets of answers,

x = π/2 ± πn, π/6 ± 2πn, or 5π/6 ± 2πn, where n is any integer.

Ex 3.4, 7 - Find general solution of sin 2x + cos x = 0

Ex 3.4, 7 – Find general solution of sin 2x + cos x = 0 – Ex 3.4, 7 Find the general solution of the equation sin 2x + cos x = 0 sin 2x + cos x = 0 Putting sin 2x = 2 sin x cos x 2 sin x cos x + cos x = 0 cos x (2sin x + 1) = 0 Hence, We find general solution of both equations separately cos x = 0 2sin x + 1 = 0 2sin x = -(1) 2sinxcosx=cosx ** Do not divide by cosx; you may lose a root ** 2sinxcosx-cosx=0. cosx(2sinx-1)=0 By the zero product property: cosx=0 ==> `x=pi/2+npi,n in ZZ` (n an integer)Solve over the Interval sin(2x)+cos(x)=0 , (0,2pi), Factor out of . Tap for more steps… Factor out of . Raise to the power of . Factor out of . Factor out of . If any individual factor on the left side of the equation is equal to , the entire expression will be equal to .

Solve algebraically: `2sinxcosx=cosx` Solve algebraically – Free Pre-Algebra, Algebra, Trigonometry, Calculus, Geometry, Statistics and Chemistry calculators step-by-stepSolve the trig equation for x from 0 to 2pi.how do you solve sin(x/2)+cosx=0 with a restriction of [0,2pi)? ** Identity: sin(x/2)=±√[(1-cosx)/2] sin(x/2)+cosx=0 sin(x/2)=cosx ±√[(1-cosx)/2]=cosx square both sides (1-cosx)/2=cos^2x 1-cosx=2cos^2x 2cos^2x+cosx-1=0 (2cosx+1)(cosx-1)=0.. 2cosx+1=0 cosx=-1/2 x=2π/3 and 4π/3 (in quadrants II and III where cos0) or cosx-1=0 cosx=1 x=0

Solve algebraically: `2sinxcosx=cosx` Solve algebraically

Solve over the Interval sin(2x)+cos(x)=0 , (0,2pi) | Mathway – Find the invCos of both sides: invCos ( cos (x) ) = invCos ( 0 ) x = 90° or 270° (and suitable multiples) geno3141 Oct 29, 2014. #2. +117458. +5. Best Answer. When cosx = 0 , sin (cos (x)) will = 0.Convert from 1 cos(x) 1 cos ( x) to sec(x) sec ( x). Divide 0 0 by 1 1. Multiply 0 0 by sec(x) sec ( x). Subtract 1 1 from both sides of the equation. Take the inverse tangent of both sides of the equation to extract x x from inside the tangent. The exact value of arctan(−1) arctan ( – 1) is − π 4 – π 4.To ask Unlimited Maths doubts download Doubtnut from – https://goo.gl/9WZjCW `cos3x-sin2x=0.`

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