?

Do the same for this but here you'll have '2x =' intead of 'x ='.

Again, post any working and any ideas that you have if you're still stuck. This is not a solutions forum and it's hard to help if I don't know your problem.

Reply 7

ztibor

Original post by Mr M

You don't know how to solve the equation

\cos 2x = 3

between 0 and 360 degrees?

Could you solve

\cos u = 3

between 0 and 720 degrees?

If so make a substitution

u = 2x

\cos 2x = 3

\cos u = 3

have no solution

because

-1 \leq \cos (anything) \leq 1

(edited 11 years ago)

Reply 8

Mr M

Study Forum Helper

Original post by ztibor

...

Well yes, we both know that was a typo.

(edited 11 years ago)

Reply 9

iamgreatness

Original post by notnek

How would you solve

\displaystyle \cos x =\frac{1}{3}

Original post by Mr M

You don't know how to solve the equation

\displaystyle \cos 2x = \frac{1}{3}

between 0 and 360 degrees?

Could you solve

\displaystyle \cos u = \frac{1}{3}

between 0 and 720 degrees?

If so make a substitution

u = 2x

im sorry i cant do it

what bit is this whats it called i will look it up in my textbook but does it have a name e.g partial fracitons

Reply 10

Mr M

Study Forum Helper

Original post by iamgreatness

im sorry i cant do it

what bit is this whats it called i will look it up in my textbook but does it have a name e.g partial fracitons

This is just Core 2 trigonometry. You really should know it inside out by the time you study Core 4.

Reply 11

Studentdk

Original post by iamgreatness

find the values of x in the range 0degrees < or equal to x < or equal 360 degrees. that satisfy sec(2x)=3

no idea what to do :/

sec(2x) = 3

=> 1/cos(2x) = 3

=> cos(2x) = 1/3

Opgave cos.jpg

click to magnify

Coordinate system contains the graphs of cos(2x) and 1/3, you can see they meet 4 times in the interval 0 to 360 degrees. So you are looking for 4 solutions.

Now use the inverse cosine (cos-1) function on your calculator to find one of the solutions.

Solution 1
cos-1(1/3) = 70.529 degrees

2x = 70.529 degrees

x = 35.264 degrees

Solution 2
Because of symmetri on the graph, solution 2 must be 180 degrees minus solution 1, solution 3 is 180 plus solution 1 and solution 4 is 360 minus solution1. (Use unit-circle to clarify this to yourself if coordinatsystem doesn't make sense)

x = 180 - 35.264 = 144.736 degrees

Solution 3

x = 180 + 35.264 = 215.264 degrees

Solution 4

x = 360 - 35.264 = 324.736 degrees

Reply 12

iamgreatness

Original post by Mr M

This is just Core 2 trigonometry. You really should know it inside out by the time you study Core 4.

i got a B in c2, duno why this is in c4 section A examples then

Reply 13

Notnek

Original post by Studentdk

...

Full solutions are not allowed in this forum. Please read the posting guide before making another post.

Reply 14

Mr M

Study Forum Helper

Original post by iamgreatness

i got a B in c2, duno why this is in c4 section A examples then

Because of the use of the reciprocal trigonometric ratio.

Reply 15

Notnek

Original post by iamgreatness

i got a B in c2, duno why this is in c4 section A examples then

Do you understand what to do now?

I don't believe that you had literally no idea how to solve

\cos x = \frac{1}{3}

in that region.

To find one solution would be a GCSE question.

Reply 16

iamgreatness

Original post by notnek

Do you understand what to do now?

I don't believe that you had literally no idea how to solve

\cos x = \frac{1}{3}

in that region.

To find one solution would be a GCSE question.

=> 1/cos(2x) = 3

=> cos(2x) = 1/3

it was just this step i had trouble with. i guess u just flip over the 1/cox(2x) to get cos2x and coz u flipped that u have to flip the 3 which makes 1/3??

Reply 17

iamgreatness

Original post by Studentdk

sec(2x) = 3

=> 1/cos(2x) = 3

=> cos(2x) = 1/3

Opgave cos.jpg

thnx altho ur not supposed to post full solutions sometimes, like arnold scwarzeneger said, u have to bend rules. thank u

Reply 18

Studentdk

Original post by notnek

Full solutions are not allowed in this forum. Please read the posting guide before making another post.

I apologise for having gone against the common spirit of this forum by posting a full solution, I was not aware of this "rule".

I do however believe that the person asking the question had received so many hints without understanding, that at some point the best help would be to see a solution.

Reply 19

Notnek

Original post by iamgreatness

=> 1/cos(2x) = 3

=> cos(2x) = 1/3

it was just this step i had trouble with. i guess u just flip over the 1/cox(2x) to get cos2x and coz u flipped that u have to flip the 3 which makes 1/3??