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help understanding C3 maths

hey, would appreciate some help:

"express

12sinx +5cosx

in the form

Rsin(x-\alpha)

"

so i have got

tan\alpha=\frac{-5}{12}

and R=13

But the answer states that

\alpha = 377.4

which I understand is -22.1.....degrees plus 360 which is also a solution for tan alpha... but I dont understand why we can just use alpha as -22 in the R(x-alpha) expression? Or 158 degrees?

I just dont fully understand how we obtain 337.4degrees and why we use it?

many thanks for any help

(edited 10 years ago)

Reply 1

brianeverit

Original post by Mr Tall

hey, would appreciate some help:

"express

12sinx +5cosx

in the form

Rsin(x-\alpha)

"

so i have got

tan\alpha=\frac{-5}{12}

and R=13

But the answer states that

\alpha = 377.4

which I understand is -22.1.....degrees plus 360 which is also a solution for tan alpha... but I dont understand why we can just use alpha as -22 in the R(x-alpha) expression? Or 158 degrees?

I just dont fully understand how we obtain 377.4degrees and why we use it?

many thanks for any help

Are you sure you have copied the answer correctly? I make alpha to be 337.4 degrees