How do you find the SINE, COSINE, and TANGENT of a 30 degree angle?

Question

and other angles?
what is the formula or rule?
my math book sux man

Answer 1

A 30°, 60°, 90° triangle has sides 1 , rt 3 , 2 and gives the following results:-

x______30°_____60°
sin x ___1/2_____(rt3) / 2
cos x___(rt3) / 2__1/2
tan x____1 / (rt3)__rt3

Sorry but I am not on my own computer and cannot access square root signs on this computer (away from home)

Answer 2

when you are plotting the Sine, Cosine, and Tangent of a triangle, you plot it on a Radial graph. The rule of S=O/H, C=A/H, and T=O/A
where sine=opposite leg/hypotenuse, cosine=adjacent leg/hypotenuse, and tangent=opposite leg/adjacent leg, from any angle in a RIGHT triangle. However, the radial graph is simply a circle with a radius of one, and you use the acute angle that comes from the origin,(0,0). So, Sine of a 30 degree angle =1/2, Cosine of a 30 degree angle=sqrt(3)/2,
and tangent, or sine/cosine, =1/sqrt(3)

Answer 3

when you have a 30 degree angle you can use the 30, 60 right triangle rule...

there is a definitel ration between the sides of the 30, 60 right triangle... that is if the side opposite the 30 degree angle has the length of a, the hypotenus will have a length of 2a, and the third side will have a length of a*sqrt3.

so if you apply the sine30... opposite/hypotenus... you get
a/2a=1/2

cosine is adjacent/hypotenus... a*sqrt3/a= sqrt3

tangent is opposite/adjacent... a/a*sqrtsqrt3=1/sqrt3... clean up the fraction you get sqrt3/3

Answer 4

For Triangle A,B,C, where Angle B is a Right angle,
side a is opposite angle A,
side b is opposite angle B, (so it's the hypotenuse since B is the right angle)
side c is opposite angle C.

sin(A) = opposite/hypotenuse = a/b
cos(A) = adjacent/hypotenuse = c/b
tan(A) = opposite/adjacent = a/c

So, physically, all you do is measure the length of each side of the right triange, and then you find the sin(), cos(), tan() functions as ratios of the lengths of the sides.

For a 30, 60, 90 right triangle, the opposite side from the 30 deg angle is exactly 1/2 the length of the hypotenuse, so,
sin(30) = 0.5

In fact the length of the sides are in the ratio, 1, 2 (3)^.5 (that's square root of 3) where the 2 is the hypotenuse.

So, cos(30) = sqroot(3)/2 = (3)^.5 / 2
tan(30) = 1/sqroot(3) = 1/(3)^.5

With a calculator, or with Excel or other spreadsheet, the thing you need to be careful of is that many of the trig functions are in terms of radians, not degrees and so you either need to set it to degrees or convert. The conversion ratio is that 360 degrees = 2*Pi radians.

Answer 5

Imagine an equilateral triangle, that is, one where all the sides are equal and all the angles are 60 degrees.

Then 30 degrees is half this, so divide the triangle in two.

Then sin(30) = opp/hyp = 1/2.
By Pythagoras, the line you've drawn is sqrt(3)/2
so cos(30) = adj/hyp = sqrt(3)/2
and tan(30) = opp/adj = 1/sqrt(3).

Hope this helps. A diagram makes it easier!
.

Answer 6

sine 45 = square root of 1/2 = 0.7071 cos 30 = square root of 1/3=0.866 tangent 60 = squre root 3 = 1.732 sin A= 0.5 means A =30°

Answer 7

trigonometric ratio valid for rightangle triangle

for sine,cosine,or others of a 30 degree mean one angle must be 30 degree

in a right triangle side opposite to 30 degree angle is half of the hypotenuous

let, hypotenuous = 1
then opp. side or perpendicular = 1/2
so,base = sq.root of(sq.of hypotenuous - sq.of per.)
=sq.root of(1 -1/4)
= sq.root of (3/4)
= sq.root of 3/2
sine 30 = p/h ..........1/2
cosine30 = b/h..............sq.root of3/2
tan30 =p/b............(1/2)/(sq.root of3/2)...........1/sq.root of 3
secant30 = 1/cosine30...........2/sq.root of3
cosecant30 = 1/sine30...............2
cotangent30 = sq.root of 3

Answer 8

Draw a representative right-angled triangle, ABC,
with angle A = 30º, angle B = 90º, and angle C = 60º.

Let side 'a' (opposite the 30º) be equal to 1 unit.
Then side 'b' (opposite 90º) will be equal to 2 units.
And side 'c' (opposite 60º) will be sqrt(3) units.

If you try and commit that to memory, then you can
easily work out sin(30º) = 1/2, cos(30º) = sqrt(3)/2
and tan(30º) = 1/sqrt(3), as well as sin, cos and tan
of 60º. That's a lot to remember, so stick with the old
maxim that a picture is worth a thousand equations!

Try to memorise the other common picture as well -
a right-angled triangle with the other angles equal to 45º.
If the legs are 1 unit each, then the hypotenuse is sqrt(2).
This will get you sin, cos and tan of 45º with ease, but
you also have to remember that sin = opp/hyp,
cos = adj/hyp and tan = opp/adj (or sin/cos).

Answer 9

Hi. Sally Could Tell Oscar Had A Heart On Always
S is sin, C is cosine, T is tangent.
S=O/H C=A/H T=O/A

This worked for me! This may explain it better http://www.phy6.org/stargaze/Strig3.htm

Answer 10

0 30 45 60 90
sin 0 1/2 1/root2 root3/2 1
cos 1 root3/2 1/root2 1/2 0
tan 0 1/root3 1 root3 not defined


this will help u!