Questions on Algebra: Trigonometry answered by real tutors!

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Question 634133: solve sin^2 x + (sinx)(cosx) = 0
Click here to see answer by Alan3354(30993)

Question 634132: solve 2sec^2 x +5tanx -3 = 0
Click here to see answer by jsmallt9(3296)

Question 634328: Tan B/2 = 15/151. I need to solve for B. I think it close to 11 degrees, but I need the exact number.
Thank you,
Click here to see answer by jsmallt9(3296)

Question 634344: Solve 2 sinx + cos2x = 2sin.sinx - 1 for 0 less thAN or equal and x greater than or equal than 2pi?

Click here to see answer by jsmallt9(3296)

Question 634419: Solve the equation for 0 less than or equal to theta less than 2 pi. Write your answer as a multiple of pi.
3 tan theta+1=2 tan theta.
Click here to see answer by ewatrrr(10682)

Question 634450: Find the exact value of sin((2x),cos(2x) given
tan(x)=-9/40, -pi/2 < x < 0
Please solve and explain.
Thanks

Click here to see answer by jsmallt9(3296)

Question 634670: what is the phase shift of the following equation?
y=-4cos(3x+π)
Click here to see answer by lwsshak3(6494)

Question 634679: Solve the following system of equations and check. Either an algebraic or graphic method will be accepted.
x²+y²=25
3x-4y=0
Click here to see answer by Alan3354(30993)

Question 634679: Solve the following system of equations and check. Either an algebraic or graphic method will be accepted.
x²+y²=25
3x-4y=0
Click here to see answer by ewatrrr(10682)

Question 634634: Find all solutions for:
4 sin^2 x - 3 = 0
Click here to see answer by lwsshak3(6494)

Question 634752: If csc t = 25/24 and tan t < 0, then sec t is equal to what?
Click here to see answer by lwsshak3(6494)

Question 634801: Find the angles of 0 degree \< x \< 360 degrees of the equation cos 4x - cos 2x
Click here to see answer by jsmallt9(3296)

Question 634797: Hi, this question has completely stumped me.
Let A,B,C be the angles of a triangle. Show that tanA+tanB+tanC=tanAtanBtanC
I've tried using identities to turn it into sin/cos but I got stuck and couldn't go any further.
I appreciate your help,
Thankyou
Click here to see answer by jsmallt9(3296)

Question 634796: Hi, I've been stuck on this one for a considerable amount of time.
=> Show that the equation 4cos(2x)-3sin(x)csc(x)^3+6 = 0, can be expressed as
8y^4-10y^2+3=0 if sin(x) = y
Hence, solve the equation for x
Thankyou for your help
Click here to see answer by ewatrrr(10682)

Question 634885: Prove that sin60/cos60=tan60. Please explain every step
Click here to see answer by Alan3354(30993)

Question 634870: 1) Prove that if 3/5 x =-9, then x=-15.
2) Prove that if 3x-2=x-8, then x=-3.
3) Prove that if 2(x-3)=8, then x=7.
4) Prove that if 3x-4=1/2 x +6, then x=4.
5) If x=y+3 and y+3=10, then x=10.
Click here to see answer by Alan3354(30993)

Question 634901: Prove that sin60/cos60=tan60
Click here to see answer by Alan3354(30993)

Question 634881: Find the angles of 0 degree \< x \< 360 degrees of the equation cos 4x - cos 2x = 0

Click here to see answer by jsmallt9(3296)

Question 634881: Find the angles of 0 degree \< x \< 360 degrees of the equation cos 4x - cos 2x = 0

Click here to see answer by Alan3354(30993)

Question 635024: Hello,
The problem that I have is that I need to verify the identity:
sin^4x+cos^4x=1-2cos^2x+2cos^4x
I started with the right hand side and I tried to group the two cosine identities
=1-2cos^2x+2cos^4x
=1-2cos^2x(1-cos^2x)
using the Pythagorean identity I got
=1-2cos^2x(sin^2x)
I'm not sure if I can use the Pythagorean identity on the first part making it
=(2sin^2x)(sin^2x)
But if I do, I'm not getting any closer to the left hand side.
Please help, or tell me if I'm at least on the right track.
Thank you
Click here to see answer by richwmiller(9135)

Question 635009: sin(3x)/sin x= 2 cos(2x)+1

cot x/(csc x+1)= (csc x -1)/cot x

Click here to see answer by Edwin McCravy(8908)

Question 635019: solve the equation for x in [0 degrees, 360 degrees), give the answer to two decimal places : 5 sin 2x = 3
Click here to see answer by jsmallt9(3296)

Question 634984: To solve this you want to write it:
x^4 + 11x^2 - 80 = 0
Click here to see answer by lwsshak3(6494)

Question 635089: Hello, I'm a little stuck...
The question is:
prove that (sin4x(1-cos2x))/(cos2x(1-cos4x)) = tanx , for 0 Thank you for your help!
Click here to see answer by jsmallt9(3296)

Question 635082: Hi, I'm terribly stuck with this question:
The angle x satisfies the equation 2tan(x)^2-5sec(x)-10=0, where x is in the second quadrant. Find the value of sec(x)

Thankyou :)
Click here to see answer by jsmallt9(3296)

Question 635145: how can i find the exact value of pie/8?
Click here to see answer by jsmallt9(3296)

Question 635237: solve over the interval [0,2π)
tan(x/2)=√(3)/3
Click here to see answer by lwsshak3(6494)

Question 635239: Find the exact value of each of the remaining trigonometric functions of θ.
Tanθ=-root(35), cosθ<0.
sinθ=?
cosθ=?
secθ=?
cscθ=?
cotθ=?
Click here to see answer by lwsshak3(6494)

Question 633997: factor and simplify the given expression. 4sec^2+8sect+4
Click here to see answer by lwsshak3(6494)

Question 635241: rewrite in terms of csc
(1/(1+cosx))+(cosx)/(1-cosx)
Click here to see answer by Edwin McCravy(8908)

Question 635241: rewrite in terms of csc
(1/(1+cosx))+(cosx)/(1-cosx)
Click here to see answer by AnlytcPhil(1276)

Question 635251: solve over the interval [0,2pi)
2sin^2(x)+cos(x)-1=0
Click here to see answer by stanbon(57307)

Question 635264: rewrite the expression in terms of the given function
(1/(1+cosx))+(cosx)/(1-cosx);csc
I assume this problem is asking to rewrite the equation in terms of cosecant. I do not know the identities to do that though
Click here to see answer by jsmallt9(3296)

Question 631664: solve the equation over interval [0,360)
(2 cos squared theta ) + (2 cos theta) - 1 = 0
Click here to see answer by lwsshak3(6494)

Question 635347: how do you do the problem 2/3 - 5/12
Click here to see answer by Maths68(1474)

Question 635351: Give the equation of the graph obtained from y = 3sin px by applying the translation (–1, –2).
Click here to see answer by tag22man(4)

Question 635392: Hi, I'm terribly stuck with this question:
The function f is defined on the domain [0,pi] by f(x)=4cos(x)+3sin(x)
a) express in the form Rcos(x-y), where 0 < y < (pi)/2
b) Hence or otherwise, write down the value of x for which f(x) takes its maximum value
Thankyou in advance
Click here to see answer by AnlytcPhil(1276)

Question 635397: Hello, I'm a little stuck...
The question is:
prove that (sin(4x)(1-cos(2x)))/(cos(2x)(1-cos(4x))) = tanx for 0 < x < (pi)/2 , x cannot equal (pi)/4
Thankyou for your help!
Click here to see answer by jsmallt9(3296)

Question 635383: Good evening,
I'm stuck on this question,
sin(x)cos(x)cos(2x)=(sin(4x))/4
I've been able to prove the left side from the right side, but I cant prove the right side from the left.
This is as far as I could get,
sin(x)cos(x)(1-2sin^2(x)
=> sin(x)cos(x)-sin^3(x)cos(x)
=> cos(x)(sin(x)-sin^3(x))
Am I on the right track?
Thankyou
Click here to see answer by jsmallt9(3296)

Question 635313: The equation h= 7(pi/3 t) models the height h in centimeters after t seconds of a weight attached to the end of a spring that has been stretched and then released.
a. Solve the equation for t.
b. Find the times at which the weight is first at a height of 1 cm, of 3 cm, and of 5 cm above the rest position. Round your answers to the nearest hundredth.
c. Find the times at which the weight is at a height of 1 cm, of 3 cm, and of 5 cm below the rest position for the second time. Round your answers to the nearest hundredth.
Click here to see answer by jsmallt9(3296)

Question 635467: Find the exact value of the expression
cos(sin^-1(square root of 5/5))
Click here to see answer by solver91311(16877)

Question 635549: If tan α = 12/5, π < α < 3 π/2, and sin β = 2/3, 0< β < π/2, find
1. sin α/2
2. cos (α+ β)
3. sin (α+ β)/2
Click here to see answer by solver91311(16877)

Question 635545: Two ocean liners leave from the same port in Puerto Rico at 10:00 a.m. One travels at a bearing of
N 46°W at 12 miles per hour, and the other travels at a bearing of S 55°W at 14 miles per hour.
Approximate the distance between them at noon the same day. Round answer to two decimal places.

Click here to see answer by Alan3354(30993)

Older solutions: 1..45, 46..90, 91..135, 136..180, 181..225, 226..270, 271..315, 316..360, 361..405, 406..450, 451..495, 496..540, 541..585, 586..630, 631..675, 676..720, 721..765, 766..810, 811..855, 856..900, 901..945, 946..990, 991..1035, 1036..1080, 1081..1125, 1126..1170, 1171..1215, 1216..1260, 1261..1305, 1306..1350, 1351..1395, 1396..1440, 1441..1485, 1486..1530, 1531..1575, 1576..1620, 1621..1665, 1666..1710, 1711..1755, 1756..1800, 1801..1845, 1846..1890, 1891..1935, 1936..1980, 1981..2025, 2026..2070, 2071..2115, 2116..2160, 2161..2205, 2206..2250, 2251..2295, 2296..2340, 2341..2385, 2386..2430, 2431..2475, 2476..2520, 2521..2565, 2566..2610, 2611..2655, 2656..2700, 2701..2745, 2746..2790, 2791..2835, 2836..2880, 2881..2925, 2926..2970, 2971..3015, 3016..3060, 3061..3105, 3106..3150, 3151..3195, 3196..3240, 3241..3285, 3286..3330, 3331..3375, 3376..3420, 3421..3465, 3466..3510, 3511..3555, 3556..3600, 3601..3645, 3646..3690, 3691..3735, 3736..3780, 3781..3825, 3826..3870, 3871..3915, 3916..3960, 3961..4005, 4006..4050, 4051..4095, 4096..4140, 4141..4185, 4186..4230, 4231..4275, 4276..4320, 4321..4365, 4366..4410, 4411..4455, 4456..4500, 4501..4545, 4546..4590, 4591..4635, 4636..4680, 4681..4725, 4726..4770, 4771..4815, 4816..4860, 4861..4905, 4906..4950, 4951..4995, 4996..5040, 5041..5085, 5086..5130, 5131..5175, 5176..5220, 5221..5265, 5266..5310, 5311..5355, 5356..5400, 5401..5445, 5446..5490, 5491..5535, 5536..5580, 5581..5625, 5626..5670, 5671..5715, 5716..5760, 5761..5805, 5806..5850, 5851..5895, 5896..5940, 5941..5985, 5986..6030, 6031..6075, 6076..6120, 6121..6165, 6166..6210, 6211..6255, 6256..6300, 6301..6345, 6346..6390, 6391..6435, 6436..6480, 6481..6525, 6526..6570, 6571..6615, 6616..6660, 6661..6705, 6706..6750, 6751..6795, 6796..6840, 6841..6885, 6886..6930, 6931..6975, 6976..7020, 7021..7065, 7066..7110, 7111..7155, 7156..7200, 7201..7245, 7246..7290, 7291..7335, 7336..7380, 7381..7425, 7426..7470, 7471..7515, 7516..7560, 7561..7605, 7606..7650, 7651..7695, 7696..7740, 7741..7785, 7786..7830, 7831..7875, 7876..7920, 7921..7965, 7966..8010, 8011..8055, 8056..8100, 8101..8145, 8146..8190, 8191..8235, 8236..8280, 8281..8325, 8326..8370, 8371..8415, 8416..8460, 8461..8505, 8506..8550, 8551..8595, 8596..8640, 8641..8685, 8686..8730, 8731..8775, 8776..8820, 8821..8865, 8866..8910, 8911..8955, 8956..9000, 9001..9045, 9046..9090, 9091..9135, 9136..9180, 9181..9225, 9226..9270, 9271..9315, 9316..9360, 9361..9405, 9406..9450, 9451..9495, 9496..9540