A Maths Help~

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A Maths Help~

Postby Firehalk » Wed Feb 29, 2012 10:19 pm

Hi, I'm currently new here and need help with an A-Maths question. Can someone kindly help?

Without using a calculator, evaluate the value of:
cos(sin-1(-4/5)+tan-1(4/7))

The answer is 37/(5sq(65))

P.S. -1 is inversed
sq is square root

Thank you.

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Re: A Maths Help~

Postby Firehalk » Wed Feb 29, 2012 11:01 pm

Some one please help me, this is urgent...

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Re: A Maths Help~

Postby mum_sugoku » Thu Mar 01, 2012 9:43 pm

Firehalk wrote:Hi, I'm currently new here and need help with an A-Maths question. Can someone kindly help?

Without using a calculator, evaluate the value of:
cos(sin-1(-4/5)+tan-1(4/7))

The answer is 37/(5sq(65))

P.S. -1 is inversed
sq is square root

Thank you.


Let x=sin-1 (-4/5), --> sin x =-4/5 (opp/hyp),
opp=-4, hyp=5, then adj=sq rt(5^2 - 4^2)=3
hence, cos x = adj/hyp=3/5

let y=tan-1 (4/7) --> tan y=4/7 (opp/adj)
opp=4, adj=7, then hyp= sq rt(7^2+4^2) =sq rt(49+16)] =sq rt(65)
hence cos y=adj/hyp=7/[sq rt(65)]
and sin y=opp/hyp=4/[sq rt(65)]

cos(sin-1(-4/5)+tan-1(4/7))
=cos (x+y)
=cosxcosy -sinxsiny
=(3/5){7/[sq rt(65)]} - (-4/5){4/[sq rt(65)]}
= 21/{5[sq rt(65)]} + 16/{5[sq rt(65)]}
=37/{5[sq rt(65)]}

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