How do i find Sine, Cosine and tangent?

Question

I was given this to do for extra credit, my math instructor did not show it done, and my book doesn't help, so how do i do this. (I will vote for best answer)...

Find the sine, cosine and tangent of the angle THETA in the following right triangle...

http://img.photobucket.com/albums/v371/MarkTivyn/3.jpg

Answer 1

Sine = opposite/hyp
Cosine = adjacent/hyp
Tangent = opposite/adjacent

Answer 2

The sine function (sin) is defined as the ratio of the leg opposite the angle to the hypotenuse.
The cosine function (cos) is defined as the ratio of the adjacent leg to the hypotenuse.
The tangent function (tan) is defined as the ratio of the opposite leg to the adjacent leg.

Now that you know the definitions, we will work on solving your problem:
sin θ = 12 / 13 (12 over 13) ≈ 0.9231
cos θ = 4 / 13 (4 over 13) ≈ 0.3077
tan θ = 12 / 4 (12 over 4) ≈ 3.0000

I hope this makes sense to you, and I hope it helps...

Answer 3

sine is the length of the leg opposite theta divided by the length of the hypotenuse. cosine is the length of the leg adjacent to theta divided by the length of the hypotenuse. tangent is the length of the side opposite theta divided by the length of the leg adjacent to theta.

Answer 4

let theta be "x"

sin x = opposite/hypotenuse
sin x = 12/13

cos x = adjacent/hypotenuse
cos x = 4/13

tan x = opposite/adjacent
tan x = 12/4 = 3

Answer 5

if it's a right angled triangle, 5,12,13 would work

c^2 = a^2 + b^2 -2abcos(C)

so for the 4,12,13, non-rightangled triangle

12^2=13^2 +4^2 - 2.13.4.cos(theta)
cos(theta) = (169+16-144)/2*4*13
= 41/104

sin(theta) = sqrt(1 - (41/104)^2) (sign is + because angle in range 0 to 90 degrees)
sqrt(1 - ((41 / 104)^2)) = 0.91901148
(calculated by pasting
sqrt(1 - ((41 / 104)^2)) =
into google search bar built-in calculator)

for a 5,12,13 rightangled triangle,
12^2 = 13^2 + 5^2 - 2.13.5cos(theta)
cos(theta) = (169+25-144)/2*5*13
= 5/13
sin(theta) = 12/13
(sign is + because angle in range 0 to 90 degrees)

Answer 6

SohCahToa
o = opposite side
h = hypotenuse
a = adjacent side
sine (abbreviated sin) = opposite/hypotenuse (Soh)
cosine (abbr. cos) = adjacent/hypotenuse (Cah)
tangent (abbr. tan) = opposite/adjacent (Toa)

Answer 7

Cos(θ) = 4/13; Sin(θ)= 12/13
Cos(Ф) = 12/13; Sin(Ф)= 4/13
Tan(θ) =Cos(θ)/Sin(θ)= 4*13/13*12
Tan(Ф) =Cos(Ф)/Sin(Ф)= 12*13/13*4

Remember this:
. . . . . . .B
. . . . . . x
.. . . . x . x
..c . x . . x
. . .x . . . x. .a
. x. . . . . x
xxxxxxxxxx
A . . b . . C

Cos(A) = b/c
Sin (A) = a/c
Tan (A) = a/b

Regard from Denmark