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# what is the best strategy to solve trig questions? watch

1. Hi everyone,

so I was doing this question in my C3 book, it's question number 9d from exercise 7F

for some reason it takes me so long to answer these questions, I could sit for 2 hours and still just complete 5-10 questions only, I get really frustrated!!

for this particular question, I arrived at the correct answer of 151.9, but then I missed the other 2 solutions!

I looked at the solution (attached pic) and found out that I actually done a step differently.
in second step my equation looked like this:

sin^2(0/2)=4sin0/2cos0/2

then I cancelled sin0/2 from sides to arrive to

tan0/2 = 4

My question is how could I avoid this error happening again, what method I can use to avoid this especially when I'm under exam conditions?

also how can improve on my speed of solving these kind of problems?

thanks
3. the question : solve sin^2(0/2) = 2sin0.
4. (Original post by ae86_trueno)
Hi everyone,
so I was doing this question in my C3 book, it's question number 9d from exercise 7F

for some reason it takes me so long to answer these questions, I could sit for 2 hours and still just complete 5-10 questions only, I get really frustrated!!

for this particular question, I arrived at the correct answer of 151.9, but then I missed the other 2 solutions!

I looked at the solution (attached pic) and found out that I actually done a step differently.
in second step my equation looked like this:

sin^2(0/2)=4sin0/2cos0/2

then I cancelled sin0/2 from sides to arrive to

tan0/2 = 4

My question is how could I avoid this error happening again, what method I can use to avoid this especially when I'm under exam conditions?

also how can improve on my speed of solving these kind of problems?

thanks
Never cancel a trig function in an equation unless you're sure that it isn't equal to 0 - always factorise instead.

E.g. 2x = x

Divide by x

2 = 1

This was incorrect cancelling because x = 0 so you're dividing by 0.

Trig example: sin(x)cos(x) = sin(x)

In this equation sin(x) = 0 is a solution so you cannot divide the equation by sin(x) (you'll lose solutions in this case). Instead factorise to give

sin(x)(cos(x) - 1) = 0

Then sin(x) = 0 or cos(x) = 1.

If you divided by sin(x) instead then you would have lost the solution sin(x) = 0.

But if you had sin(x) = 2cos(x)

Then it's fine to divide by cos(x) to give

tan(x) = 2.

This is okay because cos(x) = 0 does not satisfy the equation.

In general, dividing by trig functions to give tan(x) is usually okay (but make sure anyway) but for all other cases you have to be careful. If it's possible to factorise instead of cancelleing then always do this instead.

Also, always check your solutions at the end to make sure they work in the original equation.
5. (Original post by Notnek)
Never cancel a trig function in an equation unless you're sure that it isn't equal to 0 - always factorise instead.

E.g. 2x = x

Divide by x

2 = 1

This was incorrect cancelling because x = 0 so you're dividing by 0.

Trig example: sin(x)cos(x) = sin(x)

In this equation sin(x) = 0 is a solution so you cannot divide the equation by sin(x) (you'll lose solutions in this case). Instead factorise to give

sin(x)(cos(x) - 1) = 0

Then sin(x) = 0 or cos(x) = 1.

If you divided by sin(x) instead then you would have lost the solution sin(x) = 0.

But if you had sin(x) = 2cos(x)

Then it's fine to divide by cos(x) to give

tan(x) = 2.

This is okay because cos(x) = 0 does not satisfy the equation.

In general, dividing by trig functions to give tan(x) is usually okay (but make sure anyway) but for all other cases you have to be careful. If it's possible to factorise instead of cancelleing then always do this instead.

Also, always check your solutions at the end to make sure they work in the original equation.
thank you so much for your help, I'll keep those points in mind.
would you have any tips on solving problems faster ?
I know practice is the main thing but I've done a ton of practice and although I have improved but not too much, I still take more than usual to get around a problem!
6. I learn this from here. always try to factories first before you can cancel out and use this table below to get your all your solutions and if you don't get this u can always draw a small quadrant on the side and confirm your answer...that's How i make sure I never miss out a possibility and I've passed all my trig exams by 100%

the second table is for radians hope this helps

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