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secondary 3 | A Maths
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I just wanted to ask why 4(a) has x=360 degree. Thanks in advance
Date Posted: 4 years ago
Views: 212
What's the range given for the question? Can't see from the picture as it's cut off
The range is 0 degree to 360 degree , it includes 0 and 360
Wait I do later
If the x is 0 to 360 (inclusive)
Then the x + 60 is 60 to 420 (inclusive)
We need to look one quadrant ahead as well
Then the x + 60 is 60 to 420 (inclusive)
We need to look one quadrant ahead as well
Thank you
yes Eric is right.
if 0° ≤ x ≤ 360°,
then 60° ≤ x + 60° ≤ 420°
So,
tan²(x + 60°) = 3
tan(x + 60°) = √3 or -√3
basic angle for tan(x + 60°) = √3 is :
tan-¹(√3) = 60°
Since tan(x + 60°) is positive, it's in the first and third quadrant.
x + 60° = 60°, 180° + 60°, 360° + 60°
x + 60° = 60°, 240°, 420°
x = 0°, 180°, 360°
basic angle for tan(x + 60°) = -√3 is :
tan-¹(-√3) = -60°
Since tan(x + 60°) is negative, it's in the second and fourth quadrant.
x + 60° = 180° - 60°, 360° - 60°
x + 60° = 120°, 300°
x = 60°, 240°
So x = 0°, 60°, 180°, 240°, 360°
if 0° ≤ x ≤ 360°,
then 60° ≤ x + 60° ≤ 420°
So,
tan²(x + 60°) = 3
tan(x + 60°) = √3 or -√3
basic angle for tan(x + 60°) = √3 is :
tan-¹(√3) = 60°
Since tan(x + 60°) is positive, it's in the first and third quadrant.
x + 60° = 60°, 180° + 60°, 360° + 60°
x + 60° = 60°, 240°, 420°
x = 0°, 180°, 360°
basic angle for tan(x + 60°) = -√3 is :
tan-¹(-√3) = -60°
Since tan(x + 60°) is negative, it's in the second and fourth quadrant.
x + 60° = 180° - 60°, 360° - 60°
x + 60° = 120°, 300°
x = 60°, 240°
So x = 0°, 60°, 180°, 240°, 360°
The sad part about angles like x + 60 and x - 60 is that if an angle is rejected, we need to introduce another angle in replacement. This is unlike most equations in which rejected solutions is just left rejected.
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done
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Something like this would be good
Date Posted:
4 years ago
480° shouldn't be there
I put the 480 there to show that without the 0 to 360 stipulation, the angles can go beyond 360.
I guessed as much. Anyway students are expected to know the periodic nature of the trigo functions.
However for presentation purposes, it is best to avoid writing that and the '...' especially for the last line, because it would suggest to the marker that x goes on periodically and 480° is one of the solutions. Presentation wise, only answers in the range should be given.
AX, do take note.
However for presentation purposes, it is best to avoid writing that and the '...' especially for the last line, because it would suggest to the marker that x goes on periodically and 480° is one of the solutions. Presentation wise, only answers in the range should be given.
AX, do take note.
done
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Second one
Date Posted:
4 years ago
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