You've solved for 2x not x. Simple to fix, just half it!
The other solution is 45 + 180 from the periodicity of the tan function, then half of that gets your other answer

Reply 3

Mr M

Study Forum Helper

Original post by apronedsamurai

4=5-tan2x (0 ≤x ≤180)

I thought, it should be -1=-tan2x; 1=tan2x; =45 my textbook the answer is actually 112.5 and 22.5 Where I have went wrong?

So 2x = 45 degrees or 225 degrees.

x = ?

Reply 4

User947387

I thought perhaps I made a similar mistake with this question, but it would seem not....

2cos3x+1=0 (0 ≤x ≤360)

I simplified that to 2cos3x=60 (degrees)
cos3x=30 (degrees)

and again, Im wrong....with the first two values stated as being 40 and 80; followed by 160, 200, 280 and 320

So I am guessing then that the calculation should read cos 40; but I checked my exact values table, and cos 1/2 IS 60

Reply 5

Mr M

Study Forum Helper

Original post by apronedsamurai

2cos3x+1=0

I simplified that to 2cos3x=60

Since when did -1 = 60? You seem very confused.

Reply 6

User947387

Sorry, what I meant was; after I had subtracted the one; I had jumped to cos3x=(-)1/2. The 60 was a reference to 60 degrees; in that Cos 1/2 is 60 degrees using "exact values."

So, the associated acute angle of inverse of cos=1/2; =60 degrees.

Because cos was negative I assumed that there was solutions in the 2nd and 3rd quadrants of CAST, so 120 and 240.

0<x<360 then 3x <1080

that would mean further solutions at 120+360 and 120+360+360 and 240+360 and 240+360+360

3x =180, 240, 480, 840; and 600 and 960.
x=60, 80, 160, 200, 280, 320

However, my textbook gives the answer as being x=40 80, 160, 200, 280, 320

Not understanding the discrepancy.... :s-smilie:

(edited 9 years ago)

Reply 7

User947387

Yes, just redid it there; got the 40 myself. Thank you :smile:

Trig equations has always been a topic I was afraid of; but seem to be getting more confident with them. Thanks guys!

Reply 8

User947387

4tan3x+4=0 0<x<90

Simplified that to tax3x=-1. Associated acute angle of is 45 degrees. The answer given is simply 45 degrees. I am wondering, is this because of the following:

0<x<90 then 0<3x<270, therefore that is not a full rotation and thats why we only use the associated acute angle? I mean, the answer is negative; so it is in the 2nd and 4th quadrants, ok? 4th quadrant is 360-x; that would exceed 270 so I understand why we disregard that.

But in the 2nd quadrant, the notation is 180-x. Given that x here is 45; that would result in a net answer of 135 which is less than 270; so curious as to why its only the acute angle that is given.....?

Reply 9

TenOfThem

Original post by apronedsamurai

Hi

Because you have tan(3x) = -1 you will, indeed be looking 90<3x<180 or 270<3x<360
And, as you say - you need your 3x to be 0<3x<270

So you will need 90<3x<180

Now 180-45 = 135

SO 3x = 135

Your main issue seems to be that you are forgetting to divide by the co-efficient of x

Reply 10

User947387

Factorising trig equations is a struggle for me.

tan^2x+tanx=0
I thought that may become (tan+1)(tan-1) so than tan^2-1=0; tan =+ or - root 1 (1)

tan=+1 then 45, 135; when tan=-1; 225; 315.

But the answers given are 0,135,180,315,360; and the range is (0<x<360)

Reply 11

Slowbro93

Original post by apronedsamurai

Could you factorise for me

x^2 - x = 0

Reply 12

User947387

Coz Im stupid and **** at maths. That kept tripping me up in circle equations as well. Sorry

Reply 13

Slowbro93

Original post by apronedsamurai

Coz Im stupid and **** at maths. That kept tripping me up in circle equations as well. Sorry

Firstly

Secondly, you're not stupid, otherwise you wouldn't be doing AS maths :tongue:

I would recommend going over this page. An element of trig is being able to do simple algebra. I would recommend brushing up on this fast: http://www.cimt.plymouth.ac.uk/projects/mepres/book8/bk8i8/bk8_8i3.htm

Reply 14

User947387

X is the common factor. Oh wait, does that mean its X(x-1)? I always thought factorising meant the double brackets; the ()() so (x-1)(x+1) for example.

Reply 15

Slowbro93

Original post by apronedsamurai

X is the common factor. Oh wait, does that mean its X(x-1)? I always thought factorising meant the double brackets; the ()() so (x-1)(x+1) for example.

You are correct :yep:

And not necessarily :tongue:

Reply 16

User947387

Ok reason I thought that....QUADratic (Quad means 4) ()() is four; ergo four brackets.......Hence my confusion

Reply 17

Mr M

Study Forum Helper

Original post by apronedsamurai

Ok reason I thought that....QUADratic (Quad means 4) ()() is four; ergo four brackets.......Hence my confusion

In this case quad means square not four.

Reply 18

User947387

tanx(tanx+1)=0; tan=-1 Inverse of tan=1 (45degrees)

Negative answer, so in the 2nd and 4th quadrants. 180-45; 360-45=135, 315.

Wait.

Tanx=0; Tanx+1=0

So tanx=0;,180,360? (because thats the quadrants it is positive in/at?)

tanx+1=0; 135, 315?