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secondary 4 | A Maths
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Can you help me with part(ii), thank you!
Date Posted: 4 years ago
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Trigo is not an easy topic to understand. Let me know if you need more explanation.
Date Posted:
4 years ago
I dont understand the -2PI in red ink, how do I know how much to minus off in order to find the values of x for -PI?
Oh yes this one, good question. Wait.
The usual limits are specified as 0 to 2pi, or 0 to 360.
This time, the limits are specified as -pi to pi, or -180 to 180.
Usually we are taught to solve such questions for 0 to 360, and not -180 to 180.
What we would usually do is to find out which two Quadrants the angle belong in and then you find the angle from there. For tangent ending in positive value, the relevant Quadrants are first and third. For tangent ending in negative valued the relevant Quadrants are second or fourth.
Because this time the region wanted is -180 to 180, anything in the third quadrant or the fourth quadrant is out of range. However, -180 to 180 also contains four quadrants just like 0 to 360. Coincidentally, -180 to -90 is the third quadrant and -90 to 0 is the fourth quadrant, both from the “previous cycle” of angles.
Therefore, any value which falls into the third quadrant or the fourth quadrant will be subtracted by 360 (or 2pi) to “go back one cycle” to fit into the new range of -pi to pi. It needs to be exactly one cycle, cannot be a fraction of it, hence 360 is subtracted.
Hence, I have to subtract 2 pi, labelled in redz
This time, the limits are specified as -pi to pi, or -180 to 180.
Usually we are taught to solve such questions for 0 to 360, and not -180 to 180.
What we would usually do is to find out which two Quadrants the angle belong in and then you find the angle from there. For tangent ending in positive value, the relevant Quadrants are first and third. For tangent ending in negative valued the relevant Quadrants are second or fourth.
Because this time the region wanted is -180 to 180, anything in the third quadrant or the fourth quadrant is out of range. However, -180 to 180 also contains four quadrants just like 0 to 360. Coincidentally, -180 to -90 is the third quadrant and -90 to 0 is the fourth quadrant, both from the “previous cycle” of angles.
Therefore, any value which falls into the third quadrant or the fourth quadrant will be subtracted by 360 (or 2pi) to “go back one cycle” to fit into the new range of -pi to pi. It needs to be exactly one cycle, cannot be a fraction of it, hence 360 is subtracted.
Hence, I have to subtract 2 pi, labelled in redz
Depending on the angle chosen, if it is out of the region given, we keep subtracting 360 (if the angle is too large) or we keep adding 360 (if the angle is too small) to make the angle within the given range.
So we keep the region 0 to 180, while we must subtract all angles in the region 180 to 360 by a value of 360 (one full cycle) to meet the -180 to 0 requirement.
So we keep the region 0 to 180, while we must subtract all angles in the region 180 to 360 by a value of 360 (one full cycle) to meet the -180 to 0 requirement.
Ohhhh omg, this was so hard to understand!!!! Thank you!!!
Had the region been given as -360 to 0, of which the entire given region is one complete cycle before 0 to 360, we need to subtract 360 from all angles that we have found to make the angles within the new limit.
The angle 315 and -45 may not appear the same, but because they are in the same position in a quadrant diagram, their sines, cosines, tangents, cosecants, secants and cotangents must be equal.
The angle 315 and -45 may not appear the same, but because they are in the same position in a quadrant diagram, their sines, cosines, tangents, cosecants, secants and cotangents must be equal.
If you forget to subtract the 360 or 2pi, your angles may not be in the correct range.
1 or 2 marks will probably be deducted, but no more than that if your workings are previously valid and logical.
1 or 2 marks will probably be deducted, but no more than that if your workings are previously valid and logical.
Okayy, I’ll take note of that, thank you!! Your explanation had really enlightened me a lot:)
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