finding two unknowns from two equations??

Question

i know -4.2 + FcosӨ = 0
also 2.6 - FsinӨ = 0

how do I find F and Ө??
is it easier by calculator..or just as easy by hand??

i bet its really simple..i just cant see it!

thanks for the help

Answer 1

-4.2 + FcosӨ = 0 ------> FcosӨ = 4.2 ---#1
2.6 - FsinӨ = 0 ------> FsinӨ = 2.6 ------#2
#2/#1
tanӨ = 2.6/4.2 = 13/21
Ө = arctan(13/21)
Ө in ABC triangle A = Ө B =90 degree
AB = 13 BC = 21
use pythagorus AC = root(13^2 + 21^2) =root(610)
cos Ө is 13/root(610) in ---#1 then

F13/root(610) = 4.2
F =4.2root(610)/13

Answer 2

Here's how I would do it:

In the first equation, get F alone.
-4.2=FcosÓ¨
(-4.2)/cosÓ¨ =F

Then, substitute that into the second equation.
2.6-((-4.2)/cosÓ¨)cosÓ¨ =0

And solve using your calculator. (To get rid of cos, you should use the 2nd fuction which looks like cos^-1)

I'm not 100% sure this is exactly right, but the logic is sound.

Answer 3

-4.2 + FcosÓ¨ = 0
2.6 - FsinÓ¨ = 0

Solve the first equation for cosθ by adding 4.2 to both sides and multiplying both sides by 1/F
cosθ= 4.2/F

Solve the second for sinθ by adding -2.6 to both sides and multiplying both sides by -1/F
sinθ= 2.6/F

tanθ=sinθ/cosθ = 2.6/4.2
θ=arctan(2.6/4.2)

Since sin²θ + cos²θ = 1
F=√[(2.6)² + (4.2)²]

I try to think of everything in terms of sine and cosine. Less to remember.Fortunately for me, the problem was in terms of sine and cosine.

Answer 4

I'm using @ in place of theta.....
-4.2+Fcos @=0
hence,
Fcos @=4.2-------->(1)

and

Fsin@=2.6--------->(2)


Dividing (2) by (1)

we get

tan @ = 2.6/4.2 = 13/21

hence @= tan^-1 (13/21) Ans........


now that was tan inverse 13/21

Answer 5

divide equations, we get
2.6 = FsinÓ¨
___________
4.2 = FcosÓ¨

canceling F's, and simplify (sinÓ¨ /cosÓ¨ = tanÓ¨ )
tanÓ¨ = 2.6/4.2 = 0.619
Ó¨ = arctan 0.169
Ó¨ = 31.76 degrees

now plug into either to get F
2.6 = FsinÓ¨
2.6 = F sin(31.76)
F = 4.94

=]

.

Answer 6

Hi,

Not 100 % certain, but...
Sin and Cos have a relationship - substitute one for the other in one of the equations.
Since both formulas equal "0" then they both equal each other. Hope it helps.

Answer 7

2.6 - (F) sin(theta) = 0

-4.2 + (F) cos(theta) = 0

CAN BE SIMPLIFIED TO:

(F) cos(theta) = -4.2

(F) cos(theta) = 21 / 5

((F) cos(theta)) / cos(theta) = (21 / 5)/cos(theta)

F = 21 / ((5) cos(theta))

SUBSTITUTE F:

2.6 - (F) sin(theta) = 0

13/5 - (21 / ((5) cos(theta))) sin(theta) = 0

13/5 - ((21) tan(theta))/5 = 0

((21) tan(theta))/5 = 13/5

5 (((21) tan(theta))/5) = 5(13/5)

(21) tan(theta) = 13

((21) tan(theta))/21 = 13/21

tan(theta) = 13/21

theta = atan(13/21)

theta = 5543074961/10000000000

OR

theta = 0.5543074961

F = 21 / ((5) cos(atan(13/21)))

F = 21 / ((5)((21)SQRT(610)/610))

F = 21 / ((21)SQRT(610)/122))

F = SQRT(610)/5

F = 4.939635614

OR

F = 4.94

THEREFORE:

F, theta = {4.94, 0.55}

Answer 8

Well, since both are equal to 0, they are equal to each other, so

FcosÓ¨ = 4.2
F = 4.2/cosÓ¨

FsinÓ¨ = 2.6
F = 2.6/sinÓ¨

4.2/cosÓ¨ = 2.6/sinÓ¨

4.2sinÓ¨ = 2.6cosÓ¨
sinÓ¨/cosÓ¨ = 2.6/4.2
tanÓ¨ = 0.62
Ó¨ = invtan(0.62) = 31.75 degrees.

Fcos(31.75) = 4.2
F = 4.2/cos(31.75)
F = 4.2/0.85
F = 4.93