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AQA C2 Sector question

I am stuck on the following question 2c) from the May 2013 C2 paper. I understand it upto a certain point I work out SinD then D but in the mark scheme it says I have worked out the acute D and I need to do pi minus acute D to get the obtuse D, I do not understand this part.

Any help would be greatly appreicated thanks
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If you think about a sin wave, there are two angles per wavelength with the same value, to calculate this angle in degrees you would do 180 - theta, (e.g. type sin 30 into your calculator, then type sin 150, what do you notice?).

As this question is in radians, pi in radians= 180 in degrees.
OP, what your calculator does when you type in sin^-1(y) is to find the value of x for sin(x)=y for which the value of x is closest to the y axis (x=0). This means that when you use your calculator, sometimes you will obtain a value that is different from the actual value. As Doge (above) stated, you can work out the "correct" value by calculating pi-theta.

Hope that is clear...
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Original post by Bobjim12
If you think about a sin wave, there are two angles per wavelength with the same value, to calculate this angle in degrees you would do 180 - theta, (e.g. type sin 30 into your calculator, then type sin 150, what do you notice?).

As this question is in radians, pi in radians= 180 in degrees.


Ah I understand kinda, but how do you know when to use this?
Original post by Sayless
Ah I understand kinda, but how do you know when to use this?


If you get a question which asks you to find theta with a given range e.g. (0 < x > 360) You need to include all the angles within this range, it is a lot clearer if you sketch a graph of sin/cos/tan x and draw a straight horizontal line at a rough estimate of the point of the value of x..

I''l draw an example in a bit to make it clearer.
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Original post by Bobjim12
If you get a question which asks you to find theta with a given range e.g. (0 < x > 360) You need to include all the angles within this range, it is a lot clearer if you sketch a graph of sin/cos/tan x and draw a straight horizontal line at a rough estimate of the point of the value of x..

I''l draw an example in a bit to make it clearer.


Ah ok, so similar to the CAST circle questions?
You use this in situations where you know specifically an angle has to be obtuse or acute. In this case, the question stated that the angle is obtuse, and so it needed to be larger than pi/2. Because 1.27 is not larger than pi/2, you have to complete the process above.
Original post by Sayless
Ah ok, so similar to the CAST circle questions?



Yes, you can use the cast method, i like to think of it as this way:



the red points are the two values in x, notice if the wave were to continue, there would be more values for x.
sin x.png13.3KB
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Original post by FailedPolymath
You use this in situations where you know specifically an angle has to be obtuse or acute. In this case, the question stated that the angle is obtuse, and so it needed to be larger than pi/2. Because 1.27 is not larger than pi/2, you have to complete the process above.


Ah I understand now,thank you both for all of your help

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