Trig Function help! (1 Viewer)

SGSII · May 18, 2013

Hi Guys

Could someone please help solve this question:

Thanks

crex · May 18, 2013

$From the diagram, diameter of sun$\ =149000000\times {tan31}' \\ \pi = 180^{\circ}\\\\1^{\circ}= \frac{\pi}{180}\\\therefore {60}'=\frac{\pi}{180}\\\\{1}'= \frac{\pi}{60 \times 180}\\\\\therefore {31}'= \frac{31\pi}{10800}\\\\$when x is very small,$\ tanx\approx x \\\therefore diameter = 149000000 \times \frac{31\pi}{10800}\\\\ = 1343613$km$

EDIT: Working out is wrong, reason is below

braintic · May 18, 2013

crex said:
$From the diagram, diameter of sun$\ =149000000\times {tan31}' \\ \pi = 180^{\circ}\\\\1^{\circ}= \frac{\pi}{180}\\\therefore {60}'=\frac{\pi}{180}\\\\{1}'= \frac{\pi}{60 \times 180}\\\\\therefore {31}'= \frac{31\pi}{10800}\\\\$when x is very small,$\ tanx\approx x \\\therefore diameter = 149000000 \times \frac{31\pi}{10800}\\\\ = 1343613$km$

Answer correct, but not the working.

It should be: From the diagram, diameter of sun = 2 (149 000 000 tan 15.5').

It gives the same answer because the approximation we are using assumed sin2x = 2sinx for small angles. If you wanted a precise answer using the tan button on the calculator, your answer would be wrong.

crex · May 18, 2013

braintic said:
Answer correct, but not the working.

It should be: From the diagram, diameter of sun = 2 (149 000 000 tan 15.5').

It gives the same answer because the approximation we are using assumed sin2x = 2sinx for small angles. If you wanted a precise answer using the tan button on the calculator, your answer would be wrong.

oh kk
thanks for pointing out my mistake

SGSII · May 19, 2013

Thanks guys!
But the answer is 1343622km

Shazer2 · May 19, 2013

Can't you just split it in half and use right angle trig to find x/2, then times that by 2 to get answer?

SGSII · May 19, 2013

Shazer2 said:
Can't you just split it in half and use right angle trig to find x/2, then times that by 2 to get answer?

View attachment 28126

Thank you!

braintic · May 19, 2013

Shazer2 said:
Can't you just split it in half and use right angle trig to find x/2, then times that by 2 to get answer?

View attachment 28126

Isn't that what I did?

Shazer2 · May 19, 2013

Sorry I skimmed over your post and didn't see that, I only saw quoted part. Apologies!

Trig Function help! (1 Viewer)

SGSII

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crex

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braintic

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crex

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SGSII

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Shazer2

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SGSII

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braintic

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Shazer2

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