rand_althor
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- 2015
Re: Year 11 Mathematics 3 Unit Cambridge Question & Answer Thread
If you haven't learn the auxiliary method for combining two sine and cosine functions, you can use addition of ordinates. For each x-coordinate, add the y-coordinates of y=sinx and y=cosx. So at x=0, sin(0)=0 and cos(0)=1 -> 1+0=1.
Period: The curve starts at 1, and takes a total of 2pi units before it reaches 1 again (excluding x=pi/2). So the period is 2pi.
Amplitude: On the graph, you can see that the highest point of y=sinx+cosx is when y=sinx and y=cosx are equal. So work out the values of y=sinx and y=cosx when sinx=cosx, and add them to get the highest point. This is your amplitude.
If you haven't learn the auxiliary method for combining two sine and cosine functions, you can use addition of ordinates. For each x-coordinate, add the y-coordinates of y=sinx and y=cosx. So at x=0, sin(0)=0 and cos(0)=1 -> 1+0=1.
Period: The curve starts at 1, and takes a total of 2pi units before it reaches 1 again (excluding x=pi/2). So the period is 2pi.
Amplitude: On the graph, you can see that the highest point of y=sinx+cosx is when y=sinx and y=cosx are equal. So work out the values of y=sinx and y=cosx when sinx=cosx, and add them to get the highest point. This is your amplitude.