Questions on Algebra: Trigonometry answered by real tutors!

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Question 31277: Jane started north 2 hours ahead of Julie who was also northbound from the same location. If Julie traveled 60 mph and Jane at 40 mph, how lond did it take Julie to get 20 miles ahead of Jane?
Click here to see answer by Paul(988)

Question 31496: The equation (sin x)^6 +(cos x)^6=a has a real solution for which of the below mentioned cases:-
A.0.5<=a<=1
B.0.25<=a<=0.5
C.-1<=a<=1
D.0<=a<=0.5

Click here to see answer by venugopalramana(3286)

Question 31981: I have alot of questions similar to this, and I would like an example done for me. I don't understand the Law of Cosines very well... heres one question: If a=4, b=5, and c=7, find angle A. thanks!
Click here to see answer by stanbon(57387)

Question 31983: Expand (3cos^2theta + 2sec^2theta)^2 i figured this much but got stuck after this:
(3cos^2theta + 2sec^2theta)(3cos^2theta + 2sec^2theta)
(9cos^4theta + 4sec^2theta6cos^2theta + 4sec^4theta)
9cos^4theta + 4 (1/cos theta)^2 6cos^2theta + 4(1/cos theta)^4
i'm stuck, please help me! thanks!
Click here to see answer by stanbon(57387)

Question 31980: Solve Triangle ABC. A=90, b=4, c=7. i figured out that the hypotenuse (leg a) is the square root of 65 by using the pythagorean theorem, but how do i find angle B and C?
Click here to see answer by stanbon(57387)

Question 31998: solve the system by the method of substitution
Xsquared - Ysquared =9
X-Y=1
can you show me the steps to solve?
Click here to see answer by joey_quizan(15)

Question 32062: hi i need help seriously
\
g(x)=-2x+3 find the inverse of the function
log^381=x
5^x-4=625
27(3^x)=3^-1

Click here to see answer by stanbon(57387)

Question 32059: sketch y=3cos(2t+ 40 degrees),0 < t < 360 degrees
Click here to see answer by venugopalramana(3286)

Question 32084: Venugopalramana has kindly calculated and ploted the data from y=3cos(2t+ 40 degrees),0 < t < 360 degrees. But I do not know how the data was calculated and how he plotted the data. Could Venugopalramana or another tutor please explain the steps to calculating the data. Thankkyou
Click here to see answer by venugopalramana(3286)

Question 32124: Hi i am having trouble with some of my trigonometry problems i dont get it at all it is way over my head
1] log(b) square root of x/y^2z
2] 5^x+1=41
3] log(1/2)8=-3
4] log(3) 81=x
i hope you answer this i really need help i dont understand this
thank you by the way for the last set of questions you helped me a lot
thank you
brittny
Click here to see answer by stanbon(57387)

Question 32144: Hi i am having trouble with this problem
the directions say "change each exponential equation to its logarithmic form"
2^10=1024
i hope you can help me
thanks again
brittny
Click here to see answer by stanbon(57387)

Question 32224: Solve 11sin^2 y=13-sin^2 y for y, where 0<_y<360. How many angles satisffy this equation? Round anzwer to nearest tenth. what second quadrant satisfies this equation
what fourth quadrant angle satisfy this equation?
Click here to see answer by venugopalramana(3286)

Question 32418: Can you explain how to substitute cot (angle) with 1/root3
Click here to see answer by venugopalramana(3286)

Question 32413: the chinese used a way of measuring heighth of a mountin by viewing it from 2 diffrent locations and counculating the angle from where thay were to the top of the mountain. the frist angle measure was 8.7° and the 2nd was 7.5°. the two angles were measured from 18,325 feet apart. how tall is the mountain?
Click here to see answer by venugopalramana(3286)

Question 32560: evaluate wihout wsing a calcuator. cot60
Click here to see answer by stanbon(57387)

Question 32561: without using a calculator evealuate. csc45
Click here to see answer by Nate(3500)

Question 32568: The population of deer living in an enclosed game reserve displays regular fluctuations in size. Wildlife biologists have chosen to model the population size with a sinusoidal function. At its height the deer population is 7000, while at its low it is 2000. The time between highs and lows is 6 months. The population at the start of January, 2001 is 4500 and decreasing. Consider January, 2001 to correspond to time t = 0.
a) Model the deer population as a function of time t in months.

I'm just having a little trouble with the actual function for this one, I managed to figure out the graph I think but can't figure out how to set up the function with the numbers given. Please help if you can...
Thanks a bunch, you guys are always such a big help.
Click here to see answer by stanbon(57387)

Question 32499: prove that 1 - tan^2x = (1 - 2sin^2x)(1+tan^2x)
Click here to see answer by Fermat(127)

Question 32493: please help me with this long question. i PROMISE it really is only one question in my book, but its super long. please believe me that its only one question...
Given triangle ABC with C=48 degrees, a=12 and b=8:
a. Solve for c, rounding your answer first to the nearest tenth and then to the nearest hundredth.
b. Use the law of sines with your first answer for c to find A
c. use the law of sines with your second answer for c to find A
d. Use the law of cosines to find angle A using your first answer for c
e. use the law of cosines to find angle A using your second answer for c
f. Find angle B using the two measures found in part a.
g. is angle A acute or abtuse and why?
im so sorry this is so long, its seriously how it is in the book... its a C excersise and they're usually the hard ones, and i dont get it at all!
Click here to see answer by venugopalramana(3286)

Question 32485: Develop the formula for the tangent of the sum of angles in terms of the tangent of the separate angles alpha and beta. (I know i have to use
tan(alpha + beta) = sin(a + B)/ cos(a + B)
Click here to see answer by Fermat(127)

Question 32492: solve triangle ABC using the given info...
A=62 deg, B=34 deg, b=6... and that concludes my questions on solving triangles, i really need help. thank you so much!
Click here to see answer by stanbon(57387)

Question 32647: The perimeter of a rectangular reflecting pool in a formal garden is going to be 288 feet. If the surface area of the water is to be 4895 ft^2, give the dimensions.
Click here to see answer by checkley71(8403)

Question 32479: prove the following identity:
sin theta cos theta - sec theta sin theta = -sin^2 theta tan theta
Click here to see answer by Fermat(127)

Question 32645: solve 4x^2 - 6 = 5x i got this far and got stuck:
4x^2 - 5x - 6 = 0
(2x )(2x )
Click here to see answer by Earlsdon(6287)

Question 32646: solve x(x-1) = 3x + 2
I got x^2 - x = 3x + 2
x^2 - 4x - 2 = 0
im stuck!
Click here to see answer by mukhopadhyay(490)

Question 32644: show the steps to simplify the first expression to the second expression:
I'll let theta be equal to x.
csc^2x - cot^2x/1+tan^2x , cos^2x
thanks so much to whomever can help me with this!
Click here to see answer by venugopalramana(3286)

Question 32773: Solve each equation for all values of theta. the problem is sin(theta/2)
plus cosine(theta/2)= sqrt(2)
Click here to see answer by stanbon(57387)

Question 32478: prove the following identity:
cos2A = 2cos^2A - 1
Click here to see answer by sarah_adam(201)

Question 32864: For right ABC, angle A = 33 degrees, c = 14. Find a.
Click here to see answer by stanbon(57387)

Question 32868: A top spins 200 revolutions/minute. Find the angular velocity in radians/second.
Click here to see answer by stanbon(57387)

Question 32871: express the same function of a positive acute angle of cos 149 degrees not using a calculator.

Click here to see answer by stanbon(57387)

Question 32866: 5/4 radians= how much degress exactly?
Click here to see answer by sarah_adam(201)

Question 32872: express as the same function of a positive acute angle of csc 101 degrees not using a calculator.
Click here to see answer by stanbon(57387)

Question 32870: Express the same function of a positive acute angle of sin -315 degrees not using a calculator.
Click here to see answer by stanbon(57387)

Question 32869: Find the area of a segment of a circle whose diameter is 9 inches, if the segment has a central angle of pie/3 radians.
Click here to see answer by stanbon(57387)

Question 32867: The angular velocity of a tire is 25 radians/second. find the linear velocity of a tack stuck in the tread of the tire if the diameter of the tire is 2 feet.
Click here to see answer by stanbon(57387)

Question 32865: An aircraft carrier follows a course that has a latitude of 288 miles north and a departure of 240 miles east in one day. Find its bearing.
Click here to see answer by stanbon(57387)

Question 32767: A ramp is to be built up to a doorway. Its slope is to be 1/13. What angle will the ramp make with the horizontal? I understand that it is a right triangle, and that you probably use Sine, Cosine or Tangent, but I am not sure which one to use or what numbers.
Click here to see answer by josmiceli(9697)

Question 32482: Prove the following identity:
cos^4theta + 2cos^2theta sin^2theta + sin^4theta = 1
Click here to see answer by sarah_adam(201)

Question 32480: prove the following identity:
cos (90 deg - x) = sin x
Click here to see answer by sarah_adam(201)

Question 32892: For my college Pre-calc. class I need to prove this:
tan^3x-1/tanx-1 = sec^2x+tan x
Click here to see answer by venugopalramana(3286)

Question 32491: solve triangle ABC using the given info...
B=82 deg, a=3, c=7
Click here to see answer by venugopalramana(3286)

Question 32490: solve triangle ABC using the given info...
a=4, b=6, c=9. please help me!!! and if you could explain that would be great, im so lost!
Click here to see answer by venugopalramana(3286)

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