# Solve Sine problems with NO calc

• Feb 4th 2007, 03:15 PM
lilmolldoll41
Solve Sine problems with NO calc
how would you solve a sine problem like sin(105.5) without the use of a calculator?

Need to know by tomorrow!!!

Thanks!
• Feb 4th 2007, 03:46 PM
ThePerfectHacker
Quote:

Originally Posted by lilmolldoll41
how would you solve a sine problem like sin(105.5) without the use of a calculator?

Need to know by tomorrow!!!

Thanks!

You can use,
$\sin 105.5^o=\sin (180^o-74.5^o)=\sin 74.5^o=\sin (90^o - 15.5^o)=\cos 15.5^o$
$105.5$
Maybe you wanted to write,
$105$.
Because there is no simple method to do that.
• Feb 4th 2007, 11:51 PM
AlvinCY
There are no simple way of doing it I don't think...

There's other ways I can think of...

a) Using a sine table, not as common in Australia and in modern times where calculators are so convenient.

b) sin (105.5) = sin (90 + 15.5)... use your sine expansion, then expand sin (15.5) using sin (15 + 0.5), sin (15) is easy enough to do, just use sin (45 - 30), as for the sin (0.5), you can either remember its value, or just say it's small enough for a hand calculation to ignore... cos it only effect the answer by 0.0087, so if you give your answer to 1 decimal place, this won't affect it at all.

c) Find a sine graph, and read the value?

d) May be double angle formulae will come in handy?

e) That, or you could try the Series expansion for a Sine function: see Trigonometric function - Wikipedia, the free encyclopedia for more details... It might be easier to carry out step b), then use this for sin (0.5)

These are all just suggestions, and it only gives an approximately correct answer.
• Feb 5th 2007, 06:38 AM
ThePerfectHacker
Quote:

Originally Posted by AlvinCY
There are no simple way of doing it I don't think...

There's other ways I can think of...

a) Using a sine table, not as common in Australia and in modern times where calculators are so convenient.

b) sin (105.5) = sin (90 + 15.5)... use your sine expansion, then expand sin (15.5) using sin (15 + 0.5), sin (15) is easy enough to do, just use sin (45 - 30), as for the sin (0.5), you can either remember its value, or just say it's small enough for a hand calculation to ignore... cos it only effect the answer by 0.0087, so if you give your answer to 1 decimal place, this won't affect it at all.

c) Find a sine graph, and read the value?

d) May be double angle formulae will come in handy?

e) That, or you could try the Series expansion for a Sine function: see Trigonometric function - Wikipedia, the free encyclopedia for more details... It might be easier to carry out step b), then use this for sin (0.5)

These are all just suggestions, and it only gives an approximately correct answer.

You cannot just expand it you need to convert to radians first!
• Feb 5th 2007, 06:42 AM
AlvinCY
Quote:

Originally Posted by ThePerfectHacker
You cannot just expand it you need to convert to radians first!

What do you mean?

$sin (A+B) = sinAcosB + cosBsinA...$

That's what I meant by expand... you can do that in radians OR degrees. it really doesn't matter... as long as you're consistent.

Editted in later:

Sorry, I know what you mean now... but it's not that hard to convert 0.5 degrees to radians.
• Feb 5th 2007, 06:58 AM
ThePerfectHacker
Quote:

Originally Posted by AlvinCY

Sorry, I know what you mean now... but it's not that hard to convert 0.5 degrees to radians.

And the good thing is that since the angle is so small the first term in the Taylor series will be extremely close.
$\sin .5^o\approx \frac{.5^o\pi}{180^o}$
This is mine 45:):)th post!!!
• Feb 5th 2007, 07:00 AM
AlvinCY
Yep :-)

Man, I've been on here for a little while and I've been making soooo many mistakes... but I guess mistakes is where I'll learn from...

By the way, there's a geometry question in the other threads... which I'm still stumped on, but it's 3am, I think I'll head to bed, and either hope someone else has the solution or I'll work it out tomorrow.