A level trignometry?

prg SG

Given that sin A= 3/5 and cos B = 12/13 where A is obtuse and B is acute find exact values of cos (A+B) and cot(A-B)

**here is what i got for cos (A+B) **

cos (A+B) = cosAcosB - sinAsinB

= (12/13)(cosA) - (3/5)(sinB)

if (cos A)^2 = 1 - (sinA)^2 = 1 - (3/5)^2 = 16/25

cosA =4/5

if (sinB)^2=1- (cosB)^2 = 1 - (12/13)^2 = 25/169

sinB =5/13

therefor, cos (A+B)= (12/13)(4/5) - (3/5)(5/13) = 33/65

the answer for this at the back of the txtbook is -63/65, why is this so??

**Please explain how to do cot(A-B), for i did not get that**

eagle SG

i’m using handphone wifi at the moment, so it will be hard to answer. For a hint, A is obtuse, so cos must be negative. Try first.

wee_ws SG

Hi,

Since sin A = 3/5 and A is obtuse, you draw a right-angled triangle in the 2nd quadrant and obtain:

cos A = -4/5 and tan A = -3/4.

Since cos B = 12/13 and B is acute, you draw a right-angled triangle in the 1st quadrant and obtain:

sin B = 5/13 and tan B = 5/12.

Consider these results:

cot (A- B) = 1 / tan (A - B)

tan (A - B) = [ tan A - tan B ] / [ 1 + tan A tan B ]

Thanks!

P.S. H2 maths does not explicitly assess this knowledge.

Cheers,
Wen Shih

limywv SG

eagle SG

Oh man how come I have no idea that trigometry is actually part of the A lvl H2 syllabus?

And I think my batch (1991) is pretty screwed up. We were not taught double angle formulas, and we were the last batch to learn A maths vectors at O levels

If you stay near hougang, you can always look to wenshih for A level maths group tuition

Or me if near YCK or Tampines :D

wee_ws SG

Hi,

If you read the syllabus document carefully, you will realise that trigo knowledge is embedded in some topics, e.g. calculus. That is the reason I mentioned that trigo is not assessed explicitly.

I did my A-level in 1991 and I was taught double-angle formulae in AJC. I guess schools may have taught knowledge selectively.

Thanks and merry christmas!

Cheers,
Wen Shih