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# trig equations c2 aqa watch

1. How to go about solving trig equations such as these:Attachment 400053400063

Basically, any equation where the same function is on both sides of the equations. Im tempted to cancel it out just by doing the inverse, but i know thats incorrect and i will lose solutions. Could anyone explain the process of solving questions likr these? Thanks in advance
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2. I'm pretty sure?

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3. For the 2nd one you divide 48 by 2
Then you do 180-48 which is 132, divide that by 2
Then 360 add 48 divide 2
And finally 360 add 180 - 48 for the final answer. You should have 4 X values.
Don't know about the first one
4. (Original post by Isis_on_the_cake)

I'm pretty sure?

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Thing i dont get with that is you do the inverse of tan, but then add 180 to the answer anyway as if it was a function of tan? You got all the right solutions, i just dont quite understand why you still add 180 when you 'cancelled out' the tan function, if that makes sense.
5. (Original post by Rk2k14)
For the 2nd one you divide 48 by 2
Then you do 180-48 which is 132, divide that by 2
Then 360 add 48 divide 2
And finally 360 add 180 - 48 for the final answer. You should have 4 X values.
Don't know about the first one
So you do 180-answer, as if it was a sin function but you do the inverse of sin in the first place? Thats what i cant quite get my head around
6. (Original post by mickel_w)
Thing i dont get with that is you do the inverse of tan, but then add 180 to the answer anyway as if it was a function of tan? You got all the right solutions, i just dont quite understand why you still add 180 when you 'cancelled out' the tan function, if that makes sense.
(Original post by mickel_w)
So you do 180-answer, as if it was a sin function but you do the inverse of sin in the first place? Thats what i cant quite get my head around
Because you have an equation in , but theta must satisfy whatever trig function you started with -> ergo, you can use the appropriate formulas to find the other solutions.
7. (Original post by SamKeene)
Because you have an equation in , but theta must satisfy whatever trig function you started with -> ergo, you can use the appropriate formulas to find the other solutions.
Ok, thank you. Makes sense now
8. (Original post by mickel_w)
Ok, thank you. Makes sense now
Note even when you have a simple equation you are used to solving like:

When you solve this, you do exactly you've been doing just now, you apply the inverse to both sides:

And then you apply the various rules to find the other solutions if needed (which it isn't in the aforementioned domain).
9. Slightly different way than how the other did it I think.

10. (Original post by mickel_w)
How to go about solving trig equations such as these:Attachment 400053400063

Basically, any equation where the same function is on both sides of the equations. Im tempted to cancel it out just by doing the inverse, but i know thats incorrect and i will lose solutions. Could anyone explain the process of solving questions likr these? Thanks in advance
In cases such as these the unit circle is your best bet. A useful substitution is also handy like let v=2x.
Note we have two cases with stuff like this in sinx=sinw
infinite solutions are X=w+2npi or X=pi-w-2npi where n are integers
Using these gives all solutions. Since you have restrictions on tangents use some values of n to limit the answers.

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