Trigonometry question?

Question

First i get basic right angle trigonometry but what i don't get is when you multiply divide etc.. trig functions like

sine(30) divided by tan(45)

I can't find a site that has any trig formulas like that.The reason i am interested is that i am a roof framer and that is how you calculate the backing angle of hips in trig .But there all kinds of formulas that work generally the same way so my question is this is there a website or person who can explain

Answer 1

sin(30) is 1/2, and tan(45) is 1. So the answer to that example is 1/2.

For practical purposes, you don't want answers involving square roots, as we tend to give them in maths. Apart from a few select angles such as 30, 45, 90, 15 deg, the trig ratios aren't easy to calculate. You need a scientific calculator to evaluate something like:
sin(23) / tan(37).

Answer 2

The most common angles are 30 ,45 , 60
sin 30 = .5 sin 45 = sqrt2/2 = .707 sin 60 = sqrt(3)/2 = .866
cos 30 = .866 cos 45 = .707 cos 60 = .5
tan 30 = .577 tan45 = 1 tan 60 = 1.732

So sin 30/tan45 = .5/1 = .5

A calculator that has trig functions might be a good investment for you.

Answer 3

hmm.. am sure you could find a table of values with these kind of things.. but you need a good scientific calculator that can calculate sin(30) or cos (30) or tan (45) etc..

some angles like 30, 60, 45 have very well know values..

for example, sin 30 is 1/2

cos 30 however, is radical 3/2.. or,0.86602

and tan 45 is one... because tan is defined as sin A/ cos A..
etc.. here it gives

tan 45 = sin 45/ cos 45

now, because sin 45 = cos 45.. namely both being equal to
1/radical 2
you would just get tan 45 =1.....

Answer 4

Each is a number. sin 30 = 0.5
tan 45 = 1. sin 30/tan 45 = 0.5 / 1 = 0.5
Get a scientific calculator and it will do the figuring for you.

Answer 5

The easy answer: Get a suitable calculator, calculate the values, and do the division. Sin(30) = 0.50, tan(45) = 1.0, sin(45) = cos(45) = [sqrt(2)]/2 = 0.7071. Make a table of stuff you always encounter.

The hard answer: You need to massage things with trigonometric identities. This may or may not reduce to something more easily usable.

http://www.sosmath.com/trig/Trig5/trig5/trig5.html
http://en.wikipedia.org/wiki/List_of_trigonometric_identities
http://www.clarku.edu/~djoyce/trig/identities.html

tan(u) = sin(u)/cos(u)
tan(45) = sin(45)/cos(45)

sin(x)/tan(y) = sin(x)/[sin(y)/cos(y)]
sine(30)/tan(45) = sin(30)/[sin(45)/cos(45)]
sin(30)/[sin(45)/cos(45)] = [sin(30)][cos(45)]/sin(45)

Is [sin(x)][cos(y)]/sin(y) any easier than sin(x)/tan(y)? That can be broken up into product and divisor identities. Easier just to calculate it.

Answer 6

No general formulae for this. Just use a calculator. You can get scientific calculators very cheap these days.

For this particular example
sin 30º=0.5
tan 45º=1
so sin 30º /tan 45º=0.5