My Math Forum So confused with this

 Calculus Calculus Math Forum

 February 23rd, 2013, 01:05 AM #1 Newbie   Joined: Feb 2013 Posts: 3 Thanks: 0 So confused with this Heres the Q: Two signals are received at a satellite tracking station. They are modelled mathematically by the functions: f(t) = 10cos(16t + pi) g(t) = 10cos (20t - pi) The signals are added together, i.e. the function h(t) = f(t) + g(t) is formed. (a) Use trigonometric formulae to obtain the function h(t). (b) Obtain a graph of the function h(t). (c) Find an expression for dh/dt using the product rule and showing all workings out Now i know what a cosine wave looks like, but i really have no idea how to do this??
 February 23rd, 2013, 01:18 AM #2 Senior Member     Joined: Jul 2010 From: St. Augustine, FL., U.S.A.'s oldest city Posts: 12,211 Thanks: 521 Math Focus: Calculus/ODEs Re: So confused with this Since you are instructed to differentiate using the product rule, you need to use the sum-to-product identity: $\cos \theta + \cos \varphi= 2 \cos\left( \frac{\theta + \varphi} {2} \right) \cos\left( \frac{\theta - \varphi}{2} \right)$ Then you could use: $\cos(\theta+2\pi)=\cos(\theta)$ Can you proceed?
 February 23rd, 2013, 02:36 AM #3 Newbie   Joined: Feb 2013 Posts: 3 Thanks: 0 Re: So confused with this Ive never seen that equation. Oh dear
 February 23rd, 2013, 02:41 AM #4 Senior Member     Joined: Jul 2010 From: St. Augustine, FL., U.S.A.'s oldest city Posts: 12,211 Thanks: 521 Math Focus: Calculus/ODEs Re: So confused with this Can you apply it?
 February 23rd, 2013, 02:58 AM #5 Newbie   Joined: Feb 2013 Posts: 3 Thanks: 0 Re: So confused with this Ive tried to have a go, but im really confusing myself
 February 23rd, 2013, 10:01 AM #6 Senior Member     Joined: Jul 2010 From: St. Augustine, FL., U.S.A.'s oldest city Posts: 12,211 Thanks: 521 Math Focus: Calculus/ODEs Re: So confused with this I would begin with: $h(t)=f(t)+g(t)=10\cos(16t+\pi)+10\cos(20t-\pi)=10$$\cos(16t+\pi)+\cos(20t-\pi)$$$ Now, applying the sum-to-product identity, we have: $h(t)=10$$2\cos\(\frac{(16t+\pi)+(20t-\pi)}{2}$$\cos$$\frac{(16t+\pi)-(20t-\pi)}{2}$$\)$ $h(t)=20\cos$$\frac{36t}{2}$$\cos$$\frac{-4t+2\pi}{2}$$$ Now using the identities $\cos(\theta+2\pi)=\cos(\theta)$ and $\cos(-\theta)=\cos(\theta)$ we have: $h(t)=20\cos$$\frac{36t}{2}$$\cos$$\frac{4t}{2}$$$ $h(t)=20\cos$$18t$$\cos$$2t$$$

 Tags confused

 Thread Tools Display Modes Linear Mode

 Similar Threads Thread Thread Starter Forum Replies Last Post ccfoose Algebra 3 April 16th, 2012 09:55 PM Siedas Algebra 9 March 10th, 2012 01:29 PM katfisher1208 Algebra 1 April 20th, 2010 06:59 PM momoftwo New Users 4 August 19th, 2009 06:15 PM charlieboon Algebra 0 December 31st, 1969 04:00 PM

 Contact - Home - Forums - Cryptocurrency Forum - Top