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secondary 3 | A Maths
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need help which these questions, pls explain too as i understand nothing about double angle formula
need help with Practice now 15, questions 2,3 and 5 first. the others can wait
Date Posted: 3 years ago
Views: 254
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Practise Now 15 Q1, Q2
The rest I do another time, but no guarantee it will be tonight or tmr and only if I can remember.
The rest I do another time, but no guarantee it will be tonight or tmr and only if I can remember.
Date Posted:
3 years ago
i dont really understand q1 part iii and q2 part ii
For the change in the angle from B to B/2, you must realise that B/2 can only lie in a specific quadrant. It cannot take on multiple quadrants. Hence, you will have to reject one of the solutions in the quadratic equation, as the value of Tan B/2, for example, can’t be both negative and positive at the same time.
Also note that the double angle formula works for any pair of double angles.
For example, the base formula is
sin 2A = 2 sin A cos A
The angle 2A is twice of A. As long as one angle is twice of the other, the formula works as usual. In other words,
sin 4A = 2 sin 2A cos 2A
sin 8A = 2 sin 4A cos 4A
sin 10A = 2 sin 5A cos 5A
are valid double angle formulae. Even
sin A = 2 sin 0.5A cos 0.5A
is valid.
For example, the base formula is
sin 2A = 2 sin A cos A
The angle 2A is twice of A. As long as one angle is twice of the other, the formula works as usual. In other words,
sin 4A = 2 sin 2A cos 2A
sin 8A = 2 sin 4A cos 4A
sin 10A = 2 sin 5A cos 5A
are valid double angle formulae. Even
sin A = 2 sin 0.5A cos 0.5A
is valid.
if the question want us to find sinB/2, sinB/2 no need to be the subject?
like sinB/2 = .......
like sinB/2 = .......
The formula will be more complicated if sin B/2 is the subject. In fact, there exists a formula for it, but it’s beyond your level.
thx :) btw can you help me with questions 1,4,6, and 8 as well? dont really know what is going in here...
I do the remaining questions another day, as I am sleepy currently
sure thx :)
If I have time tonight I do the questions. I have a lot of work in recent days, but I am almost completing all of the existing ones.
Note that for future questions I may not immediately come to answer them (or even come to answer them at all), as I do need some rest days from work stuffs.
Note that for future questions I may not immediately come to answer them (or even come to answer them at all), as I do need some rest days from work stuffs.
ohh but are you free anytime this week or next week? i actually need help with proving (chapter 10.5) also as i've attempted many questions but i keep getting stucked halfway or dont even know how to start. only managed to get one question correct
You can post the question first; I completed my first part of my work beyond my packed schedule (preparing a chemistry practice for some of my students) but I realised that I forgot to factor in one more mini paper for them (to make it a complete set), so I won’t have time to do them now. I need to finish them by Sun night.
Remind me again tmr night to look at the four questions, I should be done with my work by then.
Remind me again tmr night to look at the four questions, I should be done with my work by then.
i actually need help with some questions in this post, but is it ok if i just mark this as done and post the new questions that i need help with?
I start looking at your four questions later, I should have the time today
As for the new question, it will have to depend on whether I have time or not, because I am planning to take a break on some of the days next week
As for the new question, it will have to depend on whether I have time or not, because I am planning to take a break on some of the days next week
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Q2, Q3, Q5
Date Posted:
3 years ago
i dont really understand question 3, the one on tan 3A
can you help me with the different double angle formulas? especially the one on half angle (eg A/2, 1/2B etc) as its very confusing. will really appreciate it!
For tan 3A, you need to express it as the sum of two angles 2A and A before using the addition formula for tangent.
Double angle and half angle are similar, except that instead of using 2A and A, you use A and A/2. The formula continues to work as usual as A is twice of A/2.
Double angle and half angle are similar, except that instead of using 2A and A, you use A and A/2. The formula continues to work as usual as A is twice of A/2.
i still dont understand question 3,the one on tan3A
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Q4b, Q4c, Q4d
Date Posted:
3 years ago
for 4b,why cosx=0 gives pi/2 and 3pi/2
These are special results which I have included earlier:
sin x = 0 gives 0, 180, 360
cos x = 0 gives 90, 270
tan x = 0 gives 0, 180, 360
sin x = 0 gives 0, 180, 360
cos x = 0 gives 90, 270
tan x = 0 gives 0, 180, 360
how about the one at 4c sinx=-1 gives 270
The full results
sin x = 0 gives 0, 180, 360
cos x = 0 gives 90, 270
tan x = 0 gives 0, 180, 360
sin x = 1 gives 90 (this can be seen from the graph or usual solving for sin)
cos x = 1 gives 0, 360 (this can be seen from the graph or usual solving for cos)
tan x = 1 gives 45, 225 (this can be seen from the usual solving for tan)
sin x = -1 gives 270 (this can be seen from the graph or usual solving for sin)
cos x = -1 gives 180 (this can be seen from the graph or usual solving for cos)
tan x = -1 gives 135, 315 (this can be seen from the usual solving for tan)
sin x = 0 gives 0, 180, 360
cos x = 0 gives 90, 270
tan x = 0 gives 0, 180, 360
sin x = 1 gives 90 (this can be seen from the graph or usual solving for sin)
cos x = 1 gives 0, 360 (this can be seen from the graph or usual solving for cos)
tan x = 1 gives 45, 225 (this can be seen from the usual solving for tan)
sin x = -1 gives 270 (this can be seen from the graph or usual solving for sin)
cos x = -1 gives 180 (this can be seen from the graph or usual solving for cos)
tan x = -1 gives 135, 315 (this can be seen from the usual solving for tan)
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Q6, Q8a
Date Posted:
3 years ago
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Q8b, Q8c
Date Posted:
3 years ago
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Q8d
Date Posted:
3 years ago
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The only way to simplify Tan 3A is to split them into 2A + A because this will allow us to use addition and/or double angle formulae to simplify our answers. We cannot use 2 x 1.5A to do the same job as we will get stuck halfway.
Date Posted:
3 years ago
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Q1, Q4a
The rest another time
The rest another time
Date Posted:
3 years ago
i dont really understand part f
It’s the tangent formula, but then it’s “upside down”.
The entire fraction is placed upside down, which is why the formula simplifies to 1/tan.
The entire fraction is placed upside down, which is why the formula simplifies to 1/tan.
why sinx=0 gives 0,180 and 360 degree tho
These are standard solutions:
sin x = 0 gives (in degrees) 0, 180, 360
tan x = 0 gives (in degrees) 0, 180, 360
cos x = 0 gives (in degrees) 90, 270
These can be seen from the graphs drawn for sin x, cos x and tan x, or we can also do the usual "quadrants" method by considering the "0" in sin x = 0, cos x = 0 or tan x = 0 as both a positive and a negative number before we do the usual quadrants method.
sin x = 0 gives (in degrees) 0, 180, 360
tan x = 0 gives (in degrees) 0, 180, 360
cos x = 0 gives (in degrees) 90, 270
These can be seen from the graphs drawn for sin x, cos x and tan x, or we can also do the usual "quadrants" method by considering the "0" in sin x = 0, cos x = 0 or tan x = 0 as both a positive and a negative number before we do the usual quadrants method.
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