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secondary 4 | A Maths
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Can someone pls help , thank
Date Posted: 2 years ago
Views: 361
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Your working is wrong because we can’t do the following:
tan x (3 tan x + 8) = 3
tan x = 3 or 3 tan x + 8 = 3
This is wrong because we can only do that if it is equal to 0. For example:
x (x+1) = 0
x = 0 or x+1 = 0
The rationale behind it is:
If a × b = 0, then either “a” or “b” must be 0.
If it’s not equal to 0, for example:
a × b = 10,
then “a” could be 1 and “b” could be 10, or “a” could be 2 and “b” could be 5 etc.
To solve the question, we need to let “tan x” be “u” and factorise the quadratic equation using multiplication frame (or cross-diagram) taught in Sec 2.
Let u = tan x,
3u² + 8u - 3 = 0
(3u - 1)(u + 3) = 0
Since it’s equal to 0, it’s alright to split them. Hence,
3u-1 = 0 or u+3 = 0
Change “u” back to “tan x” and do ASTC individually.
First,
3 tan x - 1 = 0
tan x = 1/3
Basic angle is 18.435°. Since 1/3 is positive, we choose the 1st and 3rd quadrant.
Therefore,
x = 18.4° (1 dp)
x = 180°+18.435°
= 198.4° (1 dp)
Second,
tan x + 3 = 0
tan x = -3
Basic angle is 71.565°. Since -3 is negative, we choose the 2nd and 4th quadrant.
Therefore,
x = 180°-71.565°
= 108.4° (1 dp)
x = 360°-71.565°
= 288.4° (1 dp)
None of the 4 answers above are out of range so we’ll accept all 4 of them:
x = 18.4°, 108.4°, 198.4°, 288.4°
tan x (3 tan x + 8) = 3
tan x = 3 or 3 tan x + 8 = 3
This is wrong because we can only do that if it is equal to 0. For example:
x (x+1) = 0
x = 0 or x+1 = 0
The rationale behind it is:
If a × b = 0, then either “a” or “b” must be 0.
If it’s not equal to 0, for example:
a × b = 10,
then “a” could be 1 and “b” could be 10, or “a” could be 2 and “b” could be 5 etc.
To solve the question, we need to let “tan x” be “u” and factorise the quadratic equation using multiplication frame (or cross-diagram) taught in Sec 2.
Let u = tan x,
3u² + 8u - 3 = 0
(3u - 1)(u + 3) = 0
Since it’s equal to 0, it’s alright to split them. Hence,
3u-1 = 0 or u+3 = 0
Change “u” back to “tan x” and do ASTC individually.
First,
3 tan x - 1 = 0
tan x = 1/3
Basic angle is 18.435°. Since 1/3 is positive, we choose the 1st and 3rd quadrant.
Therefore,
x = 18.4° (1 dp)
x = 180°+18.435°
= 198.4° (1 dp)
Second,
tan x + 3 = 0
tan x = -3
Basic angle is 71.565°. Since -3 is negative, we choose the 2nd and 4th quadrant.
Therefore,
x = 180°-71.565°
= 108.4° (1 dp)
x = 360°-71.565°
= 288.4° (1 dp)
None of the 4 answers above are out of range so we’ll accept all 4 of them:
x = 18.4°, 108.4°, 198.4°, 288.4°
Thank a lot
No prob. Hope my explanation is clear.
Can I further if can sin be replace by u
Yes, “sin x” (or “cos x” for that matter) can also be replaced by “u”, just like “tan x”.
Substituting it with “u” is just a way to factorise the expression more easily.
Substituting it with “u” is just a way to factorise the expression more easily.
Oh thank a lot
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