## Your Questions About Odds Calculator

Lisa asks…

## need trig help. need to know how to get it?

1. Find the values of the six trigonometric functions of the angle in standard position with the terminal side passing through the point P(-4, 3).

a. sin θ = -3/5; cos θ = 4/5; tan θ = 3/4; csc θ = -5/3; sec θ = 5/4; cot θ = 4/3

b. sin θ = 3/5; cos θ = -4/5; tan θ = -3/4; csc θ = 5/3; sec θ = -5/4; cot θ = -4/3

c. sin θ = 4/5; cos θ = -3/5; tan θ = -4/3; csc θ = 5/4; sec θ = -5/3; cot θ = -3/4

d. sin θ = -4/5; cos θ = 3/5; tan θ = -4/3; csc θ = -5/4; sec θ = 5/3; cot θ = -3/4

2. Find the values of the six trigonometric functions of the angle in standard position with the terminal side passing through the point P(-2, 0).

a. sin θ = -1; cos θ = 0; tan θ is undefined; csc θ = -1; sec θ is undefined; cot θ = 0

b. sin θ is undefined; cos θ = -1; tan θ is undefined; csc θ = 0; sec θ = -1; cot θ = 0

c. sin θ = 0; cos θ = -1; tan θ = 0; csc θ is undefined; sec θ = -1; cot θ is undefined

d. sin θ = 0; cos θ = -1; tan θ is undefined; csc θ is undefined; sec θ = -1; cot θ = 0

3. Given that sin θ = -1/2 for an angle in Quadrant III, find the exact value of sec θ .

a. 1/2

b. equation

c. -2

d. equation

4. Find the measurement of the reference angle of a 300 ° angle.

a. 60 °

b. -60 °

c. 30 °

d. -30 °

5. Find the measurement of the reference angle of an angle measuring 7 π /4.

a. π /2

b. – π /2

c. π /4

d. – π /4

6. Find the exact values of the six trigonometric functions of a 120 ° angle.

a. equation; equation; equation; equation; equation; equation

b. equation; equation; equation; equation; equation; equation

c. equation; equation; equation; equation; equation; equation

d. equation; equation; equation; equation; equation; equation

7. Use a **calculator** to evaluate cos 214 ° to 4 decimal places.

a. 0.5592

b. 0.8290

c. -0.5592

d. -0.8290

8. Use a **calculator** to evaluate sin(9 π /5) to 4 decimal places.

a. 0.0985

b. -0.5878

c. -0.2589

d. 0.0887

9. Find the exact value of equation

a. 1/2

b. -1/2

c. 1

d. -1

10. Find equation on a unit circle that corresponds to t = 5 π /6.

a. equation

b. equation

c. equation

d. equation

11. Evaluate equation.

a. equation

b. equation

c. 1/2

d. -1/2

12. Use a **calculator** to evaluate cot 4.

a. 0.7543

b. 0.8637

c. 1.1578

d. 0.0699

13. Evaluate equation.

a. -1/2

b. equation

c. 1/2

d. equation

14. Use a **calculator** to evaluate csc (-0.6).

a. 1.2116

b. 1.0001

c. -1.2116

d. -1.771

15. Determine whether f(x) = -sin x is even, odd, or neither.

a. even

b. odd

c. neither

### admin answers:

Some of these are deadly easy – all you need is a calculator (it even says so in the question). Others are strange because your equations are missing (they just say „equation“).

Sandy asks…

## AP CALC LIMITS!?!?!?!?!?!?!?!?!?!?!?

i got them all but one, and i can’t get it for the life of me

Let (x) = (cos x) / (x)

a Find the domain and range of f

b. Is f even, odd, or neither? Justify your answer.

c. Find the limit as x approaches infinity of f(x)

d. Use the sandwich theorem to justify your answer to part c

it specifically says show all work and DO NOT use a graphing **calculator**

thanks a million for your answer

### admin answers:

A.

-∞≤f(x)≤∞ The values of f(x) as x approaches zero from either positive or negative.

The domain is all numbers excluding 0. You could include imaginary numbers, not sure if you want to do that in this case however.

B.

An even function multiplied by an odd function produces an odd function. Thus the even function cos(x) * the odd function 1/x = the odd function cos(x) / x

c.

The functions limit as x approaches infinity (both negative and positive in this case is zero.

D.

We know that the range of cos(x) for all x (specifically for 0<x<∞) is -1 to 1.

-1 ≤ cos(x) ≤ 1

-1/x ≤ cos(x)/x ≤ 1/x

And knowing the limit of both -1/x and 1/x as x approaches infinity it must follow using the squeeze (or w/e you may call it) thm. That cos(x)/x as x approaches infinity is zero.

Q.E.D.

Please note I took out a few steps, which we're not needed for the last inequality. Please note if you want to cover negative values of x just reverse the inequality signs. This can thus be used to prove the limit of the function as x approaches negative infinity.

Maria asks…

## Music scales why are they different?

In Germany and Denmark (there maybe others), the music scale includes instead of „B“ they use „H“ Why is it referred to as this?

http://www.sengpielaudio.com/**calculator**-notenames.htm

I cannot see why they would use an odd letter (especially because the Germans like things in order– NOT being rude–)

Thanks

RR

If you look in the note English names anything that is b* IE B1 B2 B3 B4 B5 in the next section Note names german they are all ref to as „h“ I am not interested in the Hz its the two middle lists. English and German

To get it right,

this would only be used in assn‘ with brass bands, and not in general useage.

and Woodwind but not in piano and the like

### admin answers:

The brass band tradition in Germany and the Low Countries put many of the brass instruments in BUILDS tuned to flat keys . This remains in our Bb trumpet, F horn, etc. (This also was then carried over into many woodwinds in military bands.) The note Bb was referenced so often that it became an abbreviation to use B – there were few times when these band instrument would actually play in the *key of B* that uses 5 sharps!! So – when the note B natural was needed, to really specify and clarify, they used the letter H to get you attention. Worked, didn’t it?

James asks…

## Guy A or Guy B?? PLease give opinions.?

I had sex with guy A about 24 hours before my estimated ovulation the 4th ( just going by online calculators).We didnt use protection and he went in me.

On the 6th i had sex with guy B twice using condoms.

I will do a paternity test when baby is brn but til then i know the **odds** are for guy A, but how much so do you guys think?

PS.. I know i put myself in a bad situation believe me i have learned a lesson.

### admin answers:

It is probably Guy A. I certainly hope you are being open and honest with both Guy A and Guy B at this point. I’m sure it is an awkward conversation, but both of them need to know that they may (or may not) be the father…it would be horrible to spring this on them when you’ve known the possibility for 9 months.

Richard asks…

## Task 1- 3c? Homework Help- please?

The Spanish Club members are baking and selling fruit bars to raise money for a trip. They are going to make open boxes to display the bars from sheets of cardboard that are 11 inches by 17 inches. They will cut a square from each corner and fold up the sides and tape them. Find the maximum value for the volume of the box and find its dimensions.

1.This problem can be modeled by the functions v(x) = x(11 -2x)(17 -2x)

2.a. Write the equation in standard form.

The answer to ‘a’ is used through question 7.

b. Is the leading coefficient positive or negative?

c. Is the degree of the polynomial even or odd?

d. Describe the end behavior of the graph.

3. Use a graphing **calculator** to graph the equation. Hint: Try a window from −10 to 10 on the x axis, with a scale of 1, and from −500 to 500 on the y-axis, with a scale of 100.

a. How many turning points does the graph have?

b. Estimate the local maxima and minima from the graph.

4. What values of x are excluded as solutions because they do not make sense for this problem?

Use the CALC menu on your graphing **calculator** to find the approximate values of x and y at the local maximum for the graph.

What is the maximum volume of the box?

### admin answers:

2a)

v(x) = 4x^3 – 56x^2 + 187x

2b)

The leading coefficient is 4, which is positive.

2c)

The degree of the polynomial is 3, which is odd.

2d)

As x tends to infinity, v(x) will tends to infinity.

As x tends to negative infinity, v(x) will also tend to negative infinity.

3a)

2 turning points.

A polynomial with (n + 1) degree has n turning points.

3b)

Local maxima is roughly at x = 2

Local minima is roughly at x = 7

4.

All values less or equal to zero, and all values more or equal to 5.5, are rejected.

Approximate x-value of local max is ((14/3) – (sqrt(223) / 6))

Approximate y-value of local max is (1/27)*(1610 + 223sqrt(223))

Max volume of box is (1/27)*(1610 + 223sqrt(223)) inches^3

If you need a graph, look here:

http://www.wolframalpha.com/input/?i=x%2811+-2x%29%2817+-2x%29

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