cos 2x = -0.5

hey the question is

write down the number of soloutions in the range 0 <=x<=360

cos 2x = -0.5

all this stuff is so hard and im supposed to be getting an A* and i got an E :mad:

i checked the text book but its full of crap everyones telling me different ways grrrr!!!

AND
find the values of A and B such that:
for x(squared) + 10x +40 = (x+a)squared + b

i have a as 5 and b as 15 but how the hell does 5^2 = 10x???

wtf man? :mad:

i hate maths its such a pile of BS :mad:

Reply 1

insparato

15

cos 2x = -0.5

first solution comes from cos^-1 0.5 = 120

Cos is -ve in 2nd and 3rd quad.

so 2x = 120, 240, 480, 600

x = 60,120,240,300

for x(squared) + 10x +40 = (x+a)squared + b

x² + 10x + 40 ------- complete the square

(x + 5)² + 15

a = 5 b = 15

Reply 2

Nishil

OP

2

insparato

cos 2x = -0.5

first solution comes from cos^-1 0.5 = 120

Cos is -ve in 2nd and 3rd quad.

so 2x = 120, 240, 480, 600

x = 60,120,240,300

for x(squared) + 10x +40 = (x+a)squared + b

x² + 10x + 40 ------- complete the square

(x + 5)² + 15

a = 5 b = 15

firstly how am i supposed to do cos-1 on a non calc test? :mad:

and lastly i understand that but if i exapnd those brackets

(x+5)^2 + 15 i get x^2 + 25 + 15 SO HOW:

how does x^2 + 10x + 40 = X^2 + 40 we're missing the 10x!!!! :frown:

Reply 3

Christophicus

18

Nishil

hey the question is

write down the number of soloutions in the range 0 <=x<=360

cos 2x = -0.5

all this stuff is so hard and im supposed to be getting an A* and i got an E :mad:

i checked the text book but its full of crap everyones telling me different ways grrrr!!!

AND
find the values of A and B such that:
for x(squared) + 10x +40 = (x+a)squared + b

i have a as 5 and b as 15 but how the hell does 5^2 = 10x???

wtf man? :mad:

i hate maths its such a pile of BS :mad:

Firstly, calm down. lol

Firstly draw a rough sketch of y = cos2x
then draw a line y = -0.5 on the same sketch.
The number of times this line crosses the graph = number of solutions
This is 4.

x² + 10x + 40 = (x+a)² + b

Now, complete the square on the left hand side.

=> x² + 10x + 40 = (x+5)² - 25 + 40 = (x+5)² + 15
=> (x+5)² + 15 = (x+a)² + b

=> a = 5, b = 15

Reply 4

xsbrx

8

Nishil

firstly how am i supposed to do cos-1 on a non calc test? :mad:

and lastly i understand that but if i exapnd those brackets

(x+5)^2 + 15 i get x^2 + 25 + 15 SO HOW:

how does x^2 + 10x + 40 = X^2 + 40 we're missing the 10x!!!! :frown:

you are expanding that incorrectly - write it out like this so its easier
(x + 5)(x+5) + 15= x^2 + 10x + 25 + 15
= x^2 + 10x + 40

Reply 5

Nishil

OP

2

god im gonna fail maths :frown:

ok after that it says

hence or otherwise write down the minimum value of X2+10x+40......erm come again? minimum value of what fckin AQA GRRR! i cant do any of this!

Reply 6

xsbrx

8

=> (x+5)2 + 15

Well to get the smallest (min) value, that will occur when that bracket comes to zero. This will happen when x = -5

Hence the min value will be 15, which occurs when x= -5

Reply 7

Christophicus

18

Nishil

god im gonna fail maths :frown:

ok after that it says

hence or otherwise write down the minimum value of X2+10x+40......erm come again? minimum value of what fckin AQA GRRR! i cant do any of this!

x² + 10x + 40 = (x+5)² + 15

(x+5)² is greater than or equal to zero for all values of x.

Hence for minimum value of x² + 10x + 40, x = -5, so that (x+5)² = 0

So, minimum value of x² + 10x + 40

= 0 + 15 = 15

Reply 8

gyrase

3

Nishil

god im gonna fail maths :frown:

ok after that it says

hence or otherwise write down the minimum value of X2+10x+40......erm come again? minimum value of what fckin AQA GRRR! i cant do any of this!

You have to calm down and think logically. In my humble opinion, maths is not for you and you will fail it.

Anyway; from previous working you know that y = x^2 + 10x + 40 is the same as y = (x + 5)^2 + 15

Use the fact that this is a parabola, and has a vertex at (-5, 15), so the minimum value is y = 15.

Reply 9

xsbrx

8

Axon

You have to calm down and think logically. In my humble opinion, maths is not for you and you will fail it.

Anyway; from previous working you know that y = x^2 + 10x + 40 is the same as y = (x + 5)^2 + 15

Use the fact that this is a parabola, and has a vertex at (-5, 15), so the minimum value is y = 15.

Harsh (but fair!)

you are good at explaining things! :biggrin:

Reply 10

silent ninja

19

Axon

You have to calm down and think logically. In my humble opinion, maths is not for you and you will fail it.

You know that from a couple of posts? Bit harsh. He/she has exams coming up so its natural.

Nishil

firstly how am i supposed to do cos-1 on a non calc test? :mad:

maybe you need to learn the triangles, or memorise the values of cos, sine and tan for 0, 30, 45, 60, 180 etc once you know these you can work out for larger values if needed.

Reply 11

insparato

15

When did you ever say it was for a non calculator test. Firstly calm down. You need to be able to expand out of the bracket properly first. Algebraically solving cos 2x = -0.5 is a level stuff but it can be solved graphically as explained.

I dont mind explaining things at all, just ask nicely.