I need help with some math

[ThisIsMyName]

I'm doing a Pre-Calculus section review & this section has been difficult for me. So I do have quite a few questions.

 

No, they're not "Give me the answer" questions... They're "Am I doing this right?" questions.

 

The first one I have is about Graphs of Trigonometric Functions: Angles/Radians.

The instructions are: Evaluate each expression.

 

Sin 7π/6.

 

OK, the problem with this one is I'm not sure which formula I should use to solve it.

 

2. Instructions (same section): Given the measurement of a central angle, find the length of its interception arc in a circle of radius 14 centimeters. Round to the nearest tenth.

 

5π/12

What I want to do:

5π/12 x π/180

 

and then s=rө

s= 14(ans)

 

I don't have my calculator on me at the moment.... All I want to know is if that's the right track... not the answer*

 

3. Find the area of each sector given its central angle ө and the radius of the circle. Round to the nearest tenth.

 

ө= 5π/12, r= 10

 

A= 1/2r^2ө

 

Is that the formula I need?

 

4. Find each value by referring to the graph of the sine or the cosine function.

 

sin 11π

 

I have no idea. I need a formula for this one, too.

 

Think anyone can help me out?? (Again, I don't want answers...... just formulas and/or "Yeah! You're on the right track!" or "You need to rethink your process."

 

Thanks! :hyper:

[billby]

hi

The first one I have is about Graphs of Trigonometric Functions: Angles/Radians.

The instructions are: Evaluate each expression.

 

Sin 7π/6.

 

OK, the problem with this one is I'm not sure which formula I should use to solve it.

ok so by the looks of things you want a numerical value for [LATEX]sin(7\pi)[/LATEX]

this is a nice simple question that i think is supposed to get you to think about the nature of periodic functions, like the sine function.

so my advice would be, forget formule and just remember that functions like sine and cosine are periodic, ie. [LATEX]sin 0 = sin (2\pi)[/LATEX]

 

as i can't quite tell for sure what question 2 is asking, i have my suspicions but they can pipe down, so i won't offer any assistance there.

 

3. Find the area of each sector given its central angle ө and the radius of the circle. Round to the nearest tenth.

 

ө= 5π/12, r= 10

 

A= 1/2r^2ө

 

Is that the formula I need?

you can use that formula.

 

4. Find each value by referring to the graph of the sine or the cosine function.

 

sin 11π

 

I have no idea. I need a formula for this one, too.

you seem to be a bit reliant on formule, again this boils down to sine being a periodic function. so there would be two ways of doing this, simplify [LATEX]sin(11\pi)[/LATEX] as you did (or maybe will do) in question 1 or draw your graph of [LATEX]sin x[/LATEX]

 

well i hope i was of some help and didn't give away too much.

[ThisIsMyName]

Thank you, you were... But aren't formulas what math is all about?

[billby]

to a degree yes. knowing a formula is all well and good but if you can understand how the formula comes about and gives the result it does you won't be sitting in a maths exam wondering which formula to use.

[ThisIsMyName]

T.T It's a miracle I got past fourt grade multiplication, nonetheless Calculus. *cries*

 

I appriciate your help (again) THANKS! ^.^

[sanctus]

For the formula used in question 3 there is an easy "mnemotechnic" (and also shows the utility of radians). The area of a section is always [imath]{\it A}=\frac{1}{2}\theta r^2[/imath] even if the section is the full circle, then you just get the usual formula for the area of a circle; replacing [imath]\theta[/imath] with [imath]2\pi[/imath] you get just:

[math]

{\it A}_{circle}=\pi r^2

[/math]