P1 Maths (trig equations)

mik1a

I've got this practice question from www.mathsnet.net from a P1 practice paper:

Solve, for 0 < x < 180, the equation

sin(2θ+30) = 0.5

Now, this is what I tried to do. I tried not to get throw by the fact that the range has x and the equation has θ, so I assumed that x = θ (correctly?)

I changed my range by doubling all three sides and adding 30, to get:

30 < 2x + 30 < 390

then I wrote:

sin (2θ+30) = 0.5
α (acute angle) = 30
draw a quadrant diagram and find that S+ means the answer is in the first and second quadrants, so

(2θ+30) = 30, 150
therefore 2θ = 0, 120
θ = 0, 60

but the exam answer is completely different. It uses arcsin?! I've never heard of this before. I got the wrong answer as well. :frown:

Can anyone see where I went wrong?

Arcsin is also known as sin^(-1), or inverse sin, I'm sure you've seen that before...

Reply 2

OP

ah right

i didn't know you could divide by sine on its own... i thought it was part of a number, like sin30 ..

thanks. i'll try to solve it that way..

Reply 3

mik1a

ah right

i didn't know you could divide by sine on its own... i thought it was part of a number, like sin30 ..

thanks. i'll try to solve it that way..

You can't divide by sin on its own. It's a function which needs a number applied to it.

Reply 4

fishpaste

mik1a

ah right

i didn't know you could divide by sine on its own... i thought it was part of a number, like sin30 ..

thanks. i'll try to solve it that way..

What? noooooooo no no no no.

Sin^(-1) is like the opposite of sin

ie.

sin 30 = 0.5
sin^(-1) 0.5 = 30

etc.

Reply 5

boygenious

mik1a

ah right

i didn't know you could divide by sine on its own... i thought it was part of a number, like sin30 ..

thanks. i'll try to solve it that way..

i think you're getting arcsin confused with cosec. inverse sin and one over sin are different things

Reply 6

What does the answer say anyway?

Reply 7

OP

boygenious

i think you're getting arcsin confused with cosec. inverse sin and one over sin are different things

how?

inverse sin = sin^-1
one over sin = sin ^-1

isn't this right?

Reply 8

mik1a

how?

inverse sin = sin^-1
one over sin = sin ^-1

isn't this right?

For some reason they're different and not to be confused.

Oh yeah, take f(x) = sin x, then arcsin x = f^-1(x) and cosec x = 1/f(x)...

Reply 9

boygenious

mik1a

how?

inverse sin = sin^-1
one over sin = sin ^-1

isn't this right?

inverse sin (arcsin) is the inverse function of y=sinx, i.e. it is the curve y = sinx reflected in the line y = x (in the region -pi/2 < x < pi/2). whereas cosec is just y = 1/ sinx

Reply 10

OP

ok i'll take your word for it... i haven't done cosec yet but some friends from further maths said they have ...i guess its p2 or p3

it confused me when you took sin to the other side on its own. :confused:

i think i'll do it my way for now.

I just found out the questions on mathsnet change when you refresh which is probably why i got different answers to the ones they got.

Reply 11

mik1a

ok i'll take your word for it... i haven't done cosec yet but some friends from further maths said they have ...i guess its p2 or p3

it confused me when you took sin to the other side on its own. :confused:

i think i'll do it my way for now.

I just found out the questions on mathsnet change when you refresh which is probably why i got different answers to the ones they got.

Your answers seem just fine to me.

Cosecant, secant and cotangent are P2 but not too hard to understand.

cosecX or cscX = 1/sinX
secX = 1/cosX
cotX = 1/tanX

Reply 12

OP

ahh seem very simple

would that make cosec x and sec x tend to infinity when sin x and cos x touch the x axis

and inversely cot x touches the x axis at 90, 270 etc. when tan x would tend to infinity?

Reply 13

mik1a

ahh seem very simple

would that make cosec x and sec x tend to infinity when sin x and cos x touch the x axis

and inversely cot x touches the x axis at 90, 270 etc. when tan x would tend to infinity?

Wouldn't know, no textbook nearby.

Look it up on mathsnet.com...

Reply 14

username9816

ZJuwelH

Wouldn't know, no textbook nearby.

Look it up on mathsnet.com...

Irony is, I do none of this in P2 Trig.

All I do in P2 Trig is the same sort of equations etc, but using radians.

No new identities whatsoever, same 2 as in P1.

AQA Syllabus B Rules!!!!

Reply 15

fishpaste

mik1a

ahh seem very simple

would that make cosec x and sec x tend to infinity when sin x and cos x touch the x axis

and inversely cot x touches the x axis at 90, 270 etc. when tan x would tend to infinity?

Yes.

Reply 16

OP

nice easy

lol you dont do radians in P1... silly AQA !!

Reply 17

mik1a

nice easy

lol you dont do radians in P1... silly AQA !!

I did, I'm on syllabus A.

Reply 18

username9816

ZJuwelH

I did, I'm on syllabus A.

Juwel, can I ask you a question?

Would it be possible for me to do my A-Level Maths on AQA B, and do an A-Level Further Maths on OCR??

Appreciate your advice

Reply 19

username9816