Q: find the exact value of cot 15? (1 Viewer)

[Fortify]

[SOLVED] Q: find the exact value of cot 15?

I need help with: Find the exact value of Cot 15.

 

[lyounamu]

I need help with: Find the exact value of Cot 15.

cot 15 = 1/tan15 = 1/(tan45-30) = 1/(tan45-tan30/1+tan45.tan30)
= 1/(1 - 1/SQR(3)/1+1.1/SQR(3))
= 1/(1-1/SQR(3)/1+1/SQR(3))
= (1+1/SQR(3))/(1-1/SQR(3))
= (1+1/SQR(3))^2/(1-1/3)
=(1 + 1/3 + 2/SQR(3))/(2/3)
=(4+6/SQR(3))/2
= 2+3/SQR(3)

 

[bored of sc]

Cot is complimentary to tan.

So cot 15 = tan (90 - 15)
= tan 75
= tan (45 + 30)

= (tan45 + tan30) / 1 - tan45 . tan 30
= (1 + 1/root3) / 1 - 1. 1/root3
= [(root3 + 1)/ root3] / [(root3 - 1)/root3]
= (root3 + 1) / (root3 - 1)
= (root3 + 1)² / 2
= (3 + 2root3 + 1) / 2
= (4 + 2root3) / 2
= 2 + root3

EDIT: Namu, you're right but you can rationalise the denominator to make it simplier.

 

[Continuum]

Namu's method is probably better for questions like these I reckon.

 

[Fortify]

Oh, thank you!

So i was on the right track but i got lost in my own mess =\

EDIT: Namu is wrong and Bored of sc is right but i like Namu's approach.

 

[lyounamu]

Namu's method is probably better for questions like these I reckon.

Ah~It really depends. I actually found bored of sc's method very interesting and more useful in the long-run. I forgot for a second that tan was complementary to cot. If the question was like cot 60, complementary method would have helped more.

Well done, bored of sc.

 

[Continuum]

Hmm... true since there's an exact value tan 60.

 

[bubblesss]

Oh, thank you!

So i was on the right track but i got lost in my own mess =\

EDIT: Namu is wrong and Bored of sc is right but i like Namu's approach.

what are u guys goin on about isn't 2 +3/SQR3 the same as 2 +SQR3. it just has to be simplified rite? both methods are right.

 

[lyounamu]

what are u guys goin on about isn't 2 +3/SQR3 the same as 2 +SQR3. it just has to be simplified rite? both methods are right.

Yeah, I was right. I don't know what people are on about.

 

[bubblesss]

Yeah, I was right. I don't know what people are on about.

exactly. lol.:uhhuh:

 

[lyounamu]

exactly. lol.:uhhuh:

People can't see that 3/SQR(3) = SQR(3)

I think both need to re-edit their posts now, lol.

 

[Fortify]

Oh, its does =="

In the BOB it says: Cot 15 = (1 + Cos 30)/Sin 30 then etc.

How do you get (1 + Cos 30)/Sin 30 from Cot 15?

 

[lyounamu]

Oh, its does =="

In the BOB it says: Cot 15 = (1 + Cos 30)/Sin 30 then etc.

How do you get (1 + Cos 30)/Sin 30 from Cot 15?

I don't you can just state that

cot 15 = (1+cos30)/sin30

but if you see my working out, cot 15 = (1+SQR(3)/2)/(1/2)
Here, SQR(3)/2 = cos 30 and 1/2 = sin 30.

 

[bored of sc]

People can't see that 3/SQR(3) = SQR(3)

I think both need to re-edit their posts now, lol.

OH! 3 divided by square root 3. Sorry, I thought you meant 3root3. Me silly.

Will be editing now.

 

[SeftonIsAHole]

@thread starter .. go back to general maths please
cant even do taht question then couldnt even see that namu's answer was also correct

 

[ratcher0071]

cot 15 = 1/tan15 = 1/(tan45-30) = 1/(tan45-tan30/1+tan45.tan30)
= 1/(1 - 1/SQR(3)/1+1.1/SQR(3))
= 1/(1-1/SQR(3)/1+1/SQR(3))
= (1+1/SQR(3))/(1-1/SQR(3))
= (1+1/SQR(3))^2/(1-1/3)
=(1 + 1/3 + 2/SQR(3))/(2/3)
=(4+6/SQR(3))/2
= 2+3/SQR(3)