moonmaker27
New member
- Joined
- May 2, 2019
- Messages
- 2
So this is a two part exercise. I have completed the first bit, but not sure on my answer, as it appears 'strange'. The second bit I am not sure where to begin.
1a) f(x) = 10cosx - 4sinx
Given that f(x) = Rcos(x+a) where R is greater or equal to zero, and a is acute.
i) Find the value of R and the value of a
- So, after making f(x) = f(x), doing the pythagoras triangle, I got 2root29 for R and 21.8 for the acute angle.
ii) Hence solve the equation 10cosx - 4sinx = 10 for the range 0 degrees to 360 degrees (to 2dp)
- This part seemed strange because I seemed to get 0 degrees and 316.40 degrees as my two answers.
iii) Write down the minimum value of 10cosx - 4sinx
- So, I put -2root29 as the negative amplitude. Not sure if that's right.
iv) Write to 2dp the smallest possible value for x for which this minimum value occurs
- Cos graph so minimum value for x should be at 180 - a, which is 158.20 degrees.
If someone could verify those answers, that would be great. And for part b) I'm not sure I fully understand.
b) A fire alarm emits a loud oscillating signal when activated. This signal comes from two speakers, A and B. The volume of the first given is given by Va = 7cos12t, and from the second by Vb = 6sin12t. For what percentage of time is the total volume [modulus sign]Va+Vb[modulus sign] greater than 9 units?
So, my thinking was obviously to have 7cos12t + 6sin12t, but then I'm after a time, so how could it be Rcos(x-a) when it's a time I'm after and not an angle? Perhaps the exercise is seeking another trigonometric identity, but it hasn't been made clear to me. Thanks!
1a) f(x) = 10cosx - 4sinx
Given that f(x) = Rcos(x+a) where R is greater or equal to zero, and a is acute.
i) Find the value of R and the value of a
- So, after making f(x) = f(x), doing the pythagoras triangle, I got 2root29 for R and 21.8 for the acute angle.
ii) Hence solve the equation 10cosx - 4sinx = 10 for the range 0 degrees to 360 degrees (to 2dp)
- This part seemed strange because I seemed to get 0 degrees and 316.40 degrees as my two answers.
iii) Write down the minimum value of 10cosx - 4sinx
- So, I put -2root29 as the negative amplitude. Not sure if that's right.
iv) Write to 2dp the smallest possible value for x for which this minimum value occurs
- Cos graph so minimum value for x should be at 180 - a, which is 158.20 degrees.
If someone could verify those answers, that would be great. And for part b) I'm not sure I fully understand.
b) A fire alarm emits a loud oscillating signal when activated. This signal comes from two speakers, A and B. The volume of the first given is given by Va = 7cos12t, and from the second by Vb = 6sin12t. For what percentage of time is the total volume [modulus sign]Va+Vb[modulus sign] greater than 9 units?
So, my thinking was obviously to have 7cos12t + 6sin12t, but then I'm after a time, so how could it be Rcos(x-a) when it's a time I'm after and not an angle? Perhaps the exercise is seeking another trigonometric identity, but it hasn't been made clear to me. Thanks!