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# Further trigonometry c3 question watch

1. Hello I have a question...
Ik that in the example below we should use the factor formulae but how do I know which two to use from each one (numherator and denominator)!!! Is there a certain way to know or do I just guess 😕 pls help thanks xx
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2. I would get scrap and do trial and error. I know this wastes time particularly when youre doing an exam but its the only way really you can do these type of questions
3. (Original post by pondsteps)
Hello I have a question...
Ik that in the example below we should use the factor formulae but how do I know which two to use from each one (numherator and denominator)!!! Is there a certain way to know or do I just guess 😕 pls help thanks xx
Well you can clearly see that there is two sines: sin A + sin B. Now you know that you can replace A with x+2y
Use the factor formulae sin P + sin Q = sinAcosB where A is P+Q/2 and B is P-Q/2...

You have to prove the identity and it involves tan (x+y) in the right hand side and therefore they added the other two identities and left that one out on the LHS.

Also if you think about it you get tan from sin/cos. So if you leave the sin(x+y) and cos(x+y) in the denominator it would lead you to the answer - that's a way to think of it.

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4. It's as simple as that you're adding two sines, so you use sin P + sin Q. Those are just variables you can use any letter or symbol etc. If you were subtracting you'd use sin P - sin Q and it's factor formulae.

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5. (Original post by Chittesh14)
It's as simple as that you're adding two sines, so you use sin P + sin Q. Those are just variables you can use any letter or symbol etc. If you were subtracting you'd use sin P - sin Q and it's factor formulae.

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Thank u sooo much x
6. (Original post by pondsteps)
Thank u sooo much x
No problem. Please keep posting if you struggle or cannot grasp a concept. Trigonometry can be tricky but very enjoyable once understood.

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7. (Original post by Chittesh14)
No problem. Please keep posting if you struggle or cannot grasp a concept. Trigonometry can be tricky but very enjoyable once understood.

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I am struggling with question 1)b). Can u please explain what on earth is going on!!!! 😭 it was just asking to find an angle then it uses tan (A-B).. How am I supposed to know which identity to use (or when I even need to use it ) . thank u
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8. (Original post by pondsteps)
I am struggling with question 1)b). Can u please explain what on earth is going on!!!! 😭 it was just asking to find an angle then it uses tan (A-B).. How am I supposed to know which identity to use (or when I even need to use it ) . thank u
What you need to realise is when you draw the two lines. The tan of the angle created between the line and the x-axis is going to be the gradient of the line. This is because tan A is y/x where y/x is the gradient of that line. Therefore tan A is 2 and tan B is 1/3 (as y = mx + c divide all by 3).

Now if you draw the angles or work then out A > B. The angle between the two lines is the difference between the larger and smaller angle, where A is the larger angle and B is the smaller angle. So the angle made is A-B. Now you need to find tan A-B using the formulae or identity...

Eventually, you should form an equation tan (A-B) = x, where x is an unknown at the moment. You will solve for it and get two solutions and you use the one between 0<(A-B)<90 which is the secure angle - the answer.

Or alternatively you can directly do tan-1(x) or arctan(x) to the principal value which will be acute
9. (Original post by Chittesh14)
What you need to realise is when you draw the two lines. The tan of the angle created between the line and the x-axis is going to be the gradient of the line. This is because tan A is y/x where y/x is the gradient of that line. Therefore tan A is 2 and tan B is 1/3 (as y = mx + c divide all by 3).

Now if you draw the angles or work then out A > B. The angle between the two lines is the difference between the larger and smaller angle, where A is the larger angle and B is the smaller angle. So the angle made is A-B. Now you need to find tan A-B using the formulae or identity...

Eventually, you should form an equation tan (A-B) = x, where x is an unknown at the moment. You will solve for it and get two solutions and you use the one between 0<(A-B)<90 which is the secure angle - the answer.

Or alternatively you can directly do tan-1(x) or arctan(x) to the principal value which will be acute
so generally the A should be larger than the B when we are subtracting right??? because there is no negative angle..
also.. what is the gradient is negative (tan A or B ) .. do we take its abslute value or leave it as is?
10. Absolute**
11. (Original post by pondsteps)
so generally the A should be larger than the B when we are subtracting right??? because there is no negative angle..
also.. what is the gradient is negative (tan A or B ) .. do we take its abslute value or leave it as is?
The gradients are not negative though so don't worry :P. It depends on the line. The line with the greater gradient should have the greater angle. But yeah, the angle shouldn't be negative as that doesn't make sense.

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12. Oh ok!! But generally speaking I must use the absolute value of a negative gradient.. Is that correct?
13. (Original post by pondsteps)
Oh ok!! But generally speaking I must use the absolute value of a negative gradient.. Is that correct?
Yes or you could more preferred: work out the absolute value of the angle.
If gradient is -1, u get x = -45 degrees and then u take abs value to get 45 degrees

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14. (Original post by Chittesh14)
Yes or you could more preferred: work out the absolute value of the angle.
If gradient is -1, u get x = -45 degrees and then u take abs value to get 45 degrees

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Thank u very much!!!!!!
15. (Original post by pondsteps)
Thank u very much!!!!!!
No problem

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