Need Some PreCalculus Help. Please.

[GRagland]

1) Suppose that sinA=5/13, A is in quadrant 2, CosB= -1/4, and B is quadrant 2. Determine tan(A+B) and what quadrant (A+B) is in.


Thanks a lot!

 

[oniq]

Check your book

 

[Kalvin00]

Originally posted by: oniq
Check your book

Yeah. The back of the book rules 😀

 

[amnesiac]

You have a textbook that you can read, notes to study, and a teacher to ask questions of. What's your problem?

Try paying attention in class and making sure you have the teacher make clear things you're having trouble with. Then you won't be reduced to looking like a salivating retard that fell off the short bus by posting this crap on ATOT. 😀

 

[GRagland]

not in the book, please i really need the answers to these probs.

 

[Kenazo]

man those look confusing w/ an @ symbol in there. That's when you just throw in an X. 🙂

have fun. 🙂

 

[DrPizza]

Originally posted by: GRagland
I will be eternally greatful and honor you forever if you can help me out, I really need the answers for these problems, with all work shown.


1) What values of @ in [0,pi] satisfy cot@<1 ?


2) For what value of @ in [11pi/2, 6pi] is csc@=-sqrroot2 ?


3) What is the smallest positive angle, in radians, that is coterminal with -.11?


4) What are the 8 8th roots of unity, (Z to the 8th = 1)?


5) how could i prove: [2cot@]/[cot^2@-1]= tan2@

@=theta

Thanks a lot!

1. if cot<1, then tan>1..... look at the graph of tangent between 0 and Pi
2. if csc = -sqrt(2), then sin = -sqrt(2) over 2.... reference angle is Pi/4 (45 degrees)... figure out where that between your two values -will have to be 3rd or 4th quadrant because it's (-)
3. Duh.... graph where -.11 is. (4th quadrant)... since x-axis is 2Pi......
4. The eighth roots will be equally spaced around 360 degrees in the complex plane. 360 divided by 8 = 45 degrees (or pi/4 if you want). Use something similar, but opposite DeMoivre's theorem. Writing the roots in trig form, the magnitude is the eighth root of 1. The directions (of each of the 8), start at the direction of 1. (0 degrees (or radians)). Then, they're equally spaced 45 degrees. So, 1(cos0 + isin0), 1(cos45+isin45),1(cos90+isin90)........ Note, I did it in degrees because typing "pi" is a PIta
5. Starter: denominator is

 

[DrPizza]

5th isn't too hard either....

Substitute the formula for tan2@ on the right (you'll never have to touch it after this)

On the left, substitute 1/tan@ for each cot@ (or 1/tan^2@)
To get rid of the fractions in the fraction, multiply the top and bottom by tan^2@.
Done.

 

[mss242]

Originally posted by: GRagland
1) how could i prove: [2cot@]/[cot^2@-1]= tan2@

@=theta

Thanks a lot!

tan2@=(2tan@)/(1-tan^2@)

Substitute that in for the RHS and then multiply & replace the cot by 1/tan.
Then, multiply through by tan and you'll have:

(2/(1/tan^2 - 1))=2tan^2/(1 - tan^2)

Then, invert both sides and divide through by the denominators.

You'll be done

 

[DrPizza]

Inverting both sides isn't allowed in a trig proof. Instead, where you said to multiply by tan, multiply by tan squared. Done.

 

[GRagland]

okay thanks for your help guys! i got another one:

1) Suppose that sinA=5/13, A is in quadrant 2, CosB= -1/4, and B is quadrant 2. Determine tan(A+B) and what quadrant (A+B) is in.


Thanks a lot!

 

[dighn]

Originally posted by: GRagland
okay thanks for your help guys! i got another one:

1) Suppose that sinA=5/13, A is in quadrant 2, CosB= -1/4, and B is quadrant 2. Determine tan(A+B) and what quadrant (A+B) is in.


Thanks a lot!

use yoru calculator

inv-sin (dont useit directly though b/c there are 2 angles that give the same sine

 

[MrCodeDude]

ninja edit.. hold up
-- mrcodedude

 

[MrCodeDude]

m<A = 157.38°

Correct?

 

[dighn]

Originally posted by: MrCodeDude
m<A = 157.38°

Correct?

yep 🙂

 

[MrCodeDude]

m<B = 104.48° ?
-- mrcodedude

 

[MrCodeDude]

So, A+B would be in the 3rd Quadrant because the angles add up to 261.86°. Which is greater than 180° but less than 270°.

Then, tan 261.86° = 6.989 🙂
-- mrcodedude

 

[dighn]

Originally posted by: MrCodeDude
m<B = 104.48° ?
-- mrcodedude

yes supposed to be



it can be done analytically too, just need the identity for tan(a+b) wchi pbreaks it it dwon into tana and tanb, and you can get tana and tanb from sina and cosb

 

[MrCodeDude]

Now, the thing is. Do you know what I did to solve this?

Angle A
Angle B

 

[CrazyPerson]

welcome to mathland... as my physics prof says...

 

[rockyct]

See if your book is at http://www.hotmath.com and check for the problem. On many pages you can get even problems by going to the right page and replacing the problem number at the address bar.