A-LEVEL MATHS HELP! Asap

Hello, I was just wondering how on earth I am getting extra solutions when there is only 2 because I though you had to look the graph in order to fund other values.

(edited 1 year ago)

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Reply 1

tonyiptony

11

"Squaring both sides" creates extraneous solutions.

Reply 2

davros

16

Original post by skyeforster15

Hello, I was just wondering how on earth I am getting extra solutions when there is only 2 because I though you had to look the graph in order to fund other values.

you might find harmonic form a "safer" way to approach this question :smile:

Reply 3

toxicgamage56

Universities Forum Helper

19

Original post by tonyiptony

"Squaring both sides" creates extraneous solutions.

How are you meant to do the question btw?

Reply 4

davros

16

Original post by toxicgamage56

How are you meant to do the question btw?

not clear from the OP's post, but my suggestion in post #3 would be one way to go...

Reply 5

tonyiptony

11

Original post by toxicgamage56

How are you meant to do the question btw?

As davros suggests, transforming the equation into a harmonic form, i.e.

R\cos(\theta - \phi) = \text{constant}

with R and phi are constants to be found, would be the safe way*.
If you choose to square the equation like skye does, just make sure to check your answers at the end.

*How? Well if you expand the harmonic form and compare coefficients...
Also sidenote, I use cosine mostly out of habit. Some uses sine instead, and that works too. After all, cosine is just sine with a phase shift (i.e. the value of phi is different).

(edited 1 year ago)

Reply 6

toxicgamage56

Universities Forum Helper

19

Original post by tonyiptony

As davros suggests, transforming the equation into a harmonic form, i.e.

R\cos(\theta - \phi) = \text{constant}

with R and phi are constants to be found, would be the safe way*.
If you choose to square the equation like skye does, just make sure to check your answers at the end.

*How? Well if you expand the harmonic form and compare coefficients...

Ah ok I'll try this rn and tell you how it goes, thanks.

Reply 7

toxicgamage56

Universities Forum Helper

19

Original post by tonyiptony

As davros suggests, transforming the equation into a harmonic form, i.e.

R\cos(\theta - \phi) = \text{constant}

with R and phi are constants to be found, would be the safe way*.
If you choose to square the equation like skye does, just make sure to check your answers at the end.

*How? Well if you expand the harmonic form and compare coefficients...
Also sidenote, I use cosine mostly out of habit. Some uses sine instead, and that works too. After all, cosine is just sine with a phase shift (i.e. the value of phi is different).