Homework Help Thread - for all homework needs

I need some help with this math question:

For the right triangle shown below, what is the sin of angle M?
(I have no idea what sin is or how to find it)

[MrAdmiralX]

Pythagorean Theorem and Sin
12^2 = 10^2 + x^2
144-100 = x^2

x = 44^(1/2)

Sin M = x/12

Since we need the sin of the angle M it is just x/12 which is 44^(1/2)/12


Sin is the mathematical formula between the hypotenuse and opposite side. Or O/H

NVM figured it out.

[Arcadian Empire]

cos(<M)=10/12

angle M = arccos(10/12).


cos is your friend in this situation

[JOSEPHIVS MAGNVS]

There is trick we use here for that type of exercise with right triangles which works every time idk if you guys have your own version of it. Let's see how well I translate it, it would be basically to remember the word SOHCAHTOA and the meaning of each letter:

SOH means: Sin is Opposite Hypotenuse

CAH means: Cosine is Adyacent Hypotenuse

TOA means: Tanget is Opposite Adyacent

This way you remember what you need (which side of the triangle) in order to find sine, cosines and tangents. Example, in Roddney McCay's exercise he needs the sine of M so he remembers SOHCAHTOA in which Sine means Opposite (side, meaning line KL) and Hypotenuse (line KM)...

Comprende ?

[Edward Reed]

Originally Posted by Roddney McCay

I need some help with this math question:

For the right triangle shown below, what is the sin of angle M?
(I have no idea what sin is or how to find it)

when doing trig a graphing calculator is key(make sure its set to degree mode though)

using cos(adj/hyp) in this situation can save you some timelike Arcadian said
cosM=(10/12)
or
cos-1(inverse)=10/12=M

Angle M =33.55 degrees

wait till you get to circle trig I hated that stuff

edit: realized you needed sin *face palm*
double edit : realized you found out on your on

[bitermer]

i lurve sohcahtoa

I'm in need of help with another math problem. Here's the problem and choices:

Given f(x)=4x + 1 and g(x)x^2 - 2, which of the following is an expression for f(g(x))?

F. -x^2 + 4x + 1
G. x^2 + 4x - 1
H. 4x^2 - 7
J. 4x^2 - 1
K. 16x^2 + 8x - 1

I've done a little work with these equations, but never this kind of problems. Thanks in advance for helping.

[LeonidasRexII]

Originally Posted by Roddney McCay

I'm in need of help with another math problem. Here's the problem and choices:

Given f(x)=4x + 1 and g(x)x^2 - 2, which of the following is an expression for f(g(x))?

F. -x^2 + 4x + 1
G. x^2 + 4x - 1
H. 4x^2 - 7
J. 4x^2 - 1
K. 16x^2 + 8x - 1

I've done a little work with these equations, but never this kind of problems. Thanks in advance for helping.

Arc can probably explain this better, but I'll give it a go.

Whenever you see Equation: f(x) say it out the long way. In this case Equation f of (x). Using the same process you would say the second equation is f of g(x). Meaning where ever there's the x variable you substitute the g(x) equation:

f(g(x)) = 4(x^2-2) +1

Simplifying

f(g(x)) = 4x^2-8+1

Simplifying


f(g(x)) = 4x^2-7, or answer H

[Arcadian Empire]

Yeah those are called compositions. Their symbol is 'o', or a circle.

So what LRII said is right.

For example: consider two functions f, g: R -> R, where f(x) = 2x and g(x) = sin(x).

Then: (f o g)(x) = f(g(x)) = 2sin(x).

So you're just subbing in that function g into the formula for f(x). I hope that wasn't confusing.