3 years ago

If y=15 when x=2, find y when x=8

Mathematics

1 answer:

LenKa [72]3 years ago

3 0

8 ÷ 2 = 4
4× 15 = 60
y = 60

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Find the exact value of tan(x-y) if sin x=8/17 cosy = 3/5

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To solve the the question we proceed as follows:

From trigonometric laws

$(cos x)^2+(sin x)^2=1$

$sin (x-y)=sin$ $x$ $sin$ $y-sin$ $y$ $cos$ $x$

$cos (x-y)=cos$ $x$ $cos$ $y+sin$ $x$ $xin$ $y$

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$cos$ $x=sqrt(1-(sin x)^2)=sqrt(1-64/289)=sqrt(\frac{225}{289} )=\frac{15}{17}$

$cos$ $y=\frac{3}{5}$

$sin$ $x= sqrt(1- (cos x)^2)= sqrt(1-\frac{9}{25} )=sqrt(\frac{16}{25} )=\frac{4}{5}$

thus

$tan (x-y)=[sin (x-y)]/[cos (x-y)]$

=[sin x cos y-sin y cos x]/[cos x cos y+sin x sin y]

plugging in the values we obtain:

$[8/17 *3/5-4/5*15/7]/[15/17*3/5+8/17*4/5]$

simplifying

$[24/85-60/85]/[45/85+32/85]$

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EDB

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Make the marked angle, D, your center point. Find the two other points of the angle, E and B. write them in order, forwards and backwards.

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