Eric Nicholas K's answer to LockB's Secondary 3 A Maths Singapore question.
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Q6, Q7
You will face these type of questions very often in trigonometry. As far as we can, we make use of several trigonometric identities to simplify our equations. In both Q6 and Q7, we need to form quadratic-like equations which involve only a single trigonometric expression (eg cos x only) in each equation, so that we can factorise the result.
You will notice that after factorising and solving the equation, you will obtain equations of the form cos x = k, sin x = k or tan x = k for regular solving, and this is the reason why you must be able to solve the most basic of equations such as cos x = 1/2 for 0 to 2pi.
You will face these type of questions very often in trigonometry. As far as we can, we make use of several trigonometric identities to simplify our equations. In both Q6 and Q7, we need to form quadratic-like equations which involve only a single trigonometric expression (eg cos x only) in each equation, so that we can factorise the result.
You will notice that after factorising and solving the equation, you will obtain equations of the form cos x = k, sin x = k or tan x = k for regular solving, and this is the reason why you must be able to solve the most basic of equations such as cos x = 1/2 for 0 to 2pi.
Date Posted:
3 years ago
for question 6 how do we know whether the range is in radian or degree mode tho. they didnt specify whether the range 0-6 is 0degree to 6degree or 0pi to 6pi
can you help me with the list of different trigo identities as im really confused about it and the list my school gave me is messy and confusing, will really appreciate it!
As long as they did not input any degree sign, it’s radian form.
Do note, however, that 0 rad to 6 rad is not the same as 0 rad to 6pi rad.
For comparison purposes, 2pi is 6.283... when input into the calculator, so 0 rad to 6 rad is almost like 0 to 2pi.
Do note, however, that 0 rad to 6 rad is not the same as 0 rad to 6pi rad.
For comparison purposes, 2pi is 6.283... when input into the calculator, so 0 rad to 6 rad is almost like 0 to 2pi.
when they ask for number of points of intersection of the curve do we usually equate the given equations together or it depends on the question? i orginally thought they wanted us to draw out the graph...
can you help me with the list of different trigo identities as im really confused about it and the list my school gave me is messy and confusing, will really appreciate it!
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The three new trigonometric ratios to know are
1. cosec x = 1 / sin x
2. sec x = 1 / cos x
3. cot x = 1 / tan x
The five basic identities for you to know are
1. tan x = sin x / cos x
2. cot x = cos x / sin x
3. sin²x + cos²x = 1
4. tan²x + 1 = sec²x
5. cot²x + 1 = cosec²x
Do note that in some other countries, cosec x is written as csc x.
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The three new trigonometric ratios to know are
1. cosec x = 1 / sin x
2. sec x = 1 / cos x
3. cot x = 1 / tan x
The five basic identities for you to know are
1. tan x = sin x / cos x
2. cot x = cos x / sin x
3. sin²x + cos²x = 1
4. tan²x + 1 = sec²x
5. cot²x + 1 = cosec²x
Do note that in some other countries, cosec x is written as csc x.
when they ask for number of points of intersection of the curve do we usually equate the given equations together or it depends on the question? i orginally thought they wanted us to draw out the graph..
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The number of points of intersection of the curve will in general depend on the context. If a physical graph is present, you may be referring to the graph.
However, in question 6, there is no actual need to draw the graph out as the number of points of intersection is equivalent to the number of solutions of the equation.
Remember that to solve equations, graphical approaches are always available, and in many cases, algebraic approaches are available as well.
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The number of points of intersection of the curve will in general depend on the context. If a physical graph is present, you may be referring to the graph.
However, in question 6, there is no actual need to draw the graph out as the number of points of intersection is equivalent to the number of solutions of the equation.
Remember that to solve equations, graphical approaches are always available, and in many cases, algebraic approaches are available as well.
thx for guiding me! :) are you available for help today? need hrlp with addition formula which i couldnt understand anything at all
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