Trigonometry
The function f is defined for all real numbers by f(x)=sin(2x+ π/4) Find the general solution of the equation f(x)=0.
I seriously need help with this!!!
Answers
Hi there. The question tells us that sin(2x+pi/4) = 0, as both are equal to f(x). We use the inverse sin of 0 to tell us that 2x+pi/4 = 0 (the inverse sin of 0 is 0). We can just rearrange this to give. x = -pi/8. Hope this helps
31 December 2013
first, what is inside the ( ) is the "angle"then, know that angles for functions and graphs are measured in radians:0 degrees = 0 radians90 deg = pi/2 rad180 deg = pi rad360 deg = 2pi rad and so onThen, sin(angle) will be 0, everytime that (angle)= 0 or 180 or 360 and so on ( half circles and whole circles)But remember you work in radians not degrees.So sin(2x + pi/4) = 0 when (2x + pi/4) = 0, or pi, or 2pi, or 3pi . . . ... or you could write and solve, in GENERAL, (2x + pi/4) = 0 + (n times)piwhich you can do :)Solution is x=(n - 1/4) pi/2 or (n/2 - 1/8) pi
31 December 2013
Let u=2x+pi/4Then sinu=0 means that u = 0, pi or 2pi etc (ie multiples of pi, incl. -pi etc) (*)So 2x+pi/4 = 0, pi or 2pi etcHence x = -pi/8, 3pi/8 or 7pi/8 etcIf you are told that eg 0<x<pi, then pi/4<2x+pi/4<2pi+pi/4, ie pi/4<u<2pi+pi/4,so only consider u=pi & 2pi in (*) (ie no need to consider u=0 or 3pi etc)Nick
02 January 2014
Sorry, ought to have added that a general expression for -pi/8, 3pi/8 or 7pi/8 etc is (4n-1)pi/8 (as the general formula for the sequence -1, 3, 7 etc is 4n-1)Nick
02 January 2014
f(x)=sin(2x+pi/4), find for f(X)=0. This means sin(2x+pi/4)=0; 2x+pi/4=0 or pi or 2pi and so on in multiples of 2 so next will be 4pi..... This is multiples because sin of 0 or pi or 2pi or 4 pi gives zero. Hence if boundaries are not given general solution would be x= (n/2-1/8)pi where n is 0,1,2,3.... as many as you want.If gcse level maths then x=-pi/8=-0.393 (using calculator)
10 January 2014
y= 2x +pi/4sin(y)= 0 y= 2*k*pi 2x + pi/4 = 2*k*pi x= (2*k*pi - pi/4)/2
10 January 2014
Okay, so for f(x) to =0, the content of the bracket (2x+pi/4) must either =0, as sin(0) is 0, or a multiple of pi. If you look at a sine graph you'll see that the sine of pi or it's multiples is 0.So, from this we can say that 2x+pi/4=0 (or pi, 2pi etc)for the 0 example x would equal -pi/8, here's why:2x+pi/4=02x=-pi/4x=-pi/8This would most likely be your answer, especially if you are given a bounded region. Potentially there could be many answers, but if this is for GCSE it's likely -pi/8.
12 January 2014
5fqflm0s7b.png
13 February 2014
See image below for graphical solution to problem - look at where the function crosses the x-axis.
13 February 2014
ekuccwmecr.png
13 February 2014
Zoomed in version of graphical solution.
13 February 2014
Okay, we know sin(2x+pi/4)=0. Keep in mind that sin("value)"=0 only when the "value" is of the form 0+pi*K, for any integer K. For example, sin(0)=sin(pi)=sin(2*pi)=sin(3*pi)=0, and so on. So, then since the "value"=2x+pi/4, we know that:K*pi=2x+pi/4 for any integer K.Solving for x, we get x=((K-1/4)*pi)/2. for any integer K!And...didn't even need pictures. :)
11 May 2014
AS F(X)=0:. sin(2x+pi/4)=0 and we know that sin is zero at 0,180,360,...degrees i.e at kpi:. sin(2x+pi/4)=sin(kpi):. 2x+pi/4=kpi:. 2x=kpi+pi/4:.x=((4k+1)pi)/8so the correct ans is x=((4k+1)pi)/8 where k is a integer
11 May 2014
as f(x)=0:. sin(2x+pi/4)=0 and we know sin is zero at 0,180,360,.... i.e kpi where k is an integer;. sin(2x+pi/4)=sin(kpi):. 2x+pi/4=kpi;.2x=kpi-pi/4=> x=((4k-1)pi)/8 where k is an integer is the general sol
11 May 2014
Hi, I am online tutor in mathematics and masters in
mathematics I can help you in calculas1, 2,3, algebra and trigonometry,geometry
I have experience in my math lab., web assign, ale’s, Wiley
plus and all Pearson websites
I can help you in in
better manner please contact ASAP
14 May 2014
Hi, I am online tutor in mathematics and masters in
mathematics I can help you in calculas1, 2,3, algebra and trigonometry,geometry
I have experience in my math lab., web assign, ale’s, Wiley
plus and all Pearson websites
I can help you in in
better manner please contact ASAP
14 May 2014
since f(x)= 0sin(2x+pi/4) =0; (2x+pi/4)= npi; 2x= npi-pi/4; so x= npi/2- pi/8;
15 May 2014
Hey I can help you with that if u want
16 May 2014
hey sorry about the delay, if you still need help let me know.
18 June 2014
I will help you in this.
18 June 2014
contact me please, I can help you out..!!
27 June 2014
Contact me for Quality work......................Waiting, thank you
04 July 2014
f(x) = sin(2x+pi/4) also f(x) =0 so we can saysin(2x+pi/4) = 0take the inverse sin of both sides to get(ensure calculator is in radians2x+pi/4 = n*pi.subtract pi/4 from both sides to get2x = (n*pi) - (pi/4)divide both sides by 2x = (n*pi/2) - (pi/8)
04 July 2014
f(x)=0sin(2x+pi/4)=02x+pi/4=n(pi)x=1/2(n(pi)-(pi)/4)If you need more help in A level you may contact me....
21 July 2014
Tutor_hub.docx
21 July 2014
Hello,I have attached the solution of the mentioned problem. Hope it will help you.all the best.
21 July 2014
Add an answer
Similar questions
Summarise with AI: