Finding the exact value (1 Viewer)

[BlueGas]

How do I do these questions in the easiest way possible without using a graph?

 

[InteGrand]

How do I do these questions in the easiest way possible without using a graph?

 

[InteGrand]

A graph wouldn't help in finding the exact value in this one.

 

[BlueGas]

A graph wouldn't help in finding the exact value in this one.

I mean the ASTC rule, I think you have to use that rule for any method you use. I was looking at the sample answer and they done this question in two methods, I looked at the easier looking method and I didn't understand what happened in the last two lines.

 

[InteGrand]

I mean the ASTC rule, I think you have to use that rule for any method you use. I was looking at the sample answer and they done this question in two methods, I looked at the easier looking method and I didn't understand what happened in the last two lines.

Don't need ASTC, just note that tan = sin/cos, and since the tan is positive and the sin is negative (both given), the cos must be negative, since a fraction is positive if and only if its numerator and denominator have the same sign.

 

[InteGrand]

I mean the ASTC rule, I think you have to use that rule for any method you use. I was looking at the sample answer and they done this question in two methods, I looked at the easier looking method and I didn't understand what happened in the last two lines.

 

[BlueGas]

Don't need ASTC, just note that tan = sin/cos, and since the tan is positive and the sin is negative (both given), the cos must be negative, since a fraction is positive if and only if its numerator and denominator have the same sign.

What happened in the last two lines of the working out though? There's more to this working out but I understand the rest but not the last two lines.

 

[BlueGas]

How did they make cos^2theta the subject?

 

[InteGrand]

How did they make cos^2theta the subject?

Simple rearrangement of the previous equation: isolate all cos^2 theta terms to one side and then divide both sides by the coefficient of cos^2 theta.

It's exactly the same as making X the subject in:1 – X = 49X

 

[BlueGas]

Simple rearrangement of the previous equation: isolate all cos^2 theta terms to one side and then divide both sides by the coefficient of cos^2 theta.

It's exactly the same as making X the subject in:1 – X = 49X

Now I get it, I honestly don't know how I didn't realise 49cos^2theta + cos^2theta = 50cos^2theta, made it so much simple making cos^2theta = x, thanks!

 

[Startales]

I'd draw a triangle and use SOH CAH TOA. I.e. tanx= 7/1, therefore hypotenuse is 7^2+1^2 which is root 50. Therefore exact value of cosx is 1/root 50 but the angle lies in the 3rd quadrant since tanx>0 and sinx<0. Hence cosx is -ve 1/root 50

 

[BlueGas]

I'd draw a triangle and use SOH CAH TOA. I.e. tanx= 7/1, therefore hypotenuse is 7^2+1^2 which is root 50. Therefore exact value of cosx is 1/root 50 but the angle lies in the 3rd quadrant since tanx>0 and sinx<0. Hence cosx is -ve 1/root 50

Can you just explain the part how you know it lies in the 3rd quadrant?

 

[leehuan]

Tan is positive (note that 7 is a positive number) and sine is negative

This ONLY occurs in the third quadrant according to:
A- All positive
S- Sine positive
T - Tangent positive
C - Cosine positive

Then, because you want cosine in the third quadrant, it must be negative.
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Personally, I reckon if you can actually remember ASTC and what IS positive WHERE, that's easier than using a Pythagorean identity.

 

[BlueGas]

Tan is positive (note that 7 is a positive number) and sine is negative

This ONLY occurs in the third quadrant according to:
A- All positive
S- Sine positive
T - Tangent positive
C - Cosine positive

Then, because you want cosine in the third quadrant, it must be negative.
_______________________________
Personally, I reckon if you can actually remember ASTC and what IS positive WHERE, that's easier than using a Pythagorean identity.

Ah I get it now, yeah I find it much easier too using the ASTC rule, I think startales should have said "since tanx >0, and cosx < 0" instead of "since tanx > 0 and sinx<0", but I get it now

But I haven't seen not many if any HSC questions on these, is that normal?

 

[leehuan]

Ah I get it now, yeah I find it much easier too using the ASTC rule, I think startales should have said "since tanx >0, and cosx < 0" instead of "since tanx > 0 and sinx<0", but I get it now

But I haven't seen not many if any HSC questions on these, is that normal?

They're more common in prelim. And multiple choice.

 

[InteGrand]

I think startales should have said "since tanx >0, and cosx < 0" instead of "since tanx > 0 and sinx<0"

sin x is also negative though, in fact, this is the fact directly given to us in the question, which is why startales said it.