Questions on Algebra: Trigonometry answered by real tutors!

Tutors Answer Your Questions about Trigonometry-basics (FREE)

Question 278878: (Tough) Find the lengths of both circular arcs of the unit circle connecting (-sqrt2 / 2 , sqrt2 / 2) and the point whose radius makes an angle of 2.05 radians with the positive horizontal axis ( What are the answers rounded to 3 decimal places)
Click here to see answer by Alan3354(31538)

Question 278904: at 12:00 both the minute hand and the hour hand point to 12. At what precise time ( to the nearest minute) would the hour hand be perpendicular to the minute hand? (the angle between them would be pi/2 or 90 degrees)
Click here to see answer by checkley77(12569)

Question 279019: sin(x)tan(x/2)=1-cosx
how to i prove this identity?
Click here to see answer by Edwin McCravy(8999)

Question 279149: Two streets meet at an angle of 52 degrees. If a triangular lot has frontages of 60 m and 65 m on the two streets, what is the perimeter of the lot?
Click here to see answer by Theo(3504)

Question 279196: prove:
sinx-1/sinx = -cosx/tanx
Click here to see answer by Alan3354(31538)

Question 279377: What is the exact value of sin^2 pi/6 -2 sin pi/6 cos pi/6 + cos^2 (-pi/6)?
The answer I got is 2 + sqrt3/2. Did I do it right. This question is driving me crazy the other answer I got was 2 - sqrt3?? Help please cause I'm obviously doing something wrong.
Click here to see answer by scott8148(6628)

Question 279481: 9 cos^2 theta + 3 cos theta =0, where 90 degrees < theta < 180 degrees, what is the value of theta, correct to the nearest tenth? This is what I did but my answer is wrong cause it's suppose to be in degrees.9 cos^2 theta + 3 cos theta =0 Then I subtracted 3 cos theta from both sides so 9 cos^2 theta= -3 cos theta Then I divided both sides by cos 3 theta so cos theta = -1/3. I don't think I understand how to do the question since it's not in degrees. Any ideas?? Thanks
Click here to see answer by scott8148(6628)

Question 279675: I am extremely confused about a problem I'm working on. I can't seem to get the right answer.
A kite flier wondered how high her kite was flying. She used a protractor to measure an angle of 45 degrees from level ground to the kite string. If she used a full 105 yard spool of string, how high, in feet, was the kite? Round the answer to 3 decimal places. (Disregard the string sag and the height of the string reel above the ground.)
I know the correct answer is 222.739 ft, but I don't know how that's possible. Every time I try to solve it I get 24.789ft. Please help!
Click here to see answer by nerdybill(7011)

Question 279782: give the amplitude and period of the sine function y = 2 sin x

Click here to see answer by Alan3354(31538)

Question 279811: using the substituion method 9x+7y=9 and x=57-7y
Click here to see answer by JenniferTutors(83)

Question 280342: what are the (x,y) coordinats of the intersection of the lines determined by the equations 2x - 7y = 41 and x + 3y = -12
Click here to see answer by Alan3354(31538)

Question 280342: what are the (x,y) coordinats of the intersection of the lines determined by the equations 2x - 7y = 41 and x + 3y = -12
Click here to see answer by hemendraagrawal9@gmail.com(1)

Question 280360: Find all the solutions in the interval [0, 2pi): sin2x = cos x
Click here to see answer by stanbon(57984)

Question 280440: A kite flying 20 feet above the ground is attached to a string 80 feet long. The string is being held by a person on the ground. Find the angle between the string and the ground.
Click here to see answer by mananth(12270)

Question 280769: sin^2 x - cos^2 x = 2sin^2-1
Click here to see answer by Alan3354(31538)

Question 281002: sketch the triangle and use the law of cosines to find the indicated value.round your answer ro the nearest hundreth.
22)find the angle opposite the longest side in a triangle with sides of 43 ft ,48ft, and 65ft.
Click here to see answer by stanbon(57984)

Question 281086: (toughness- 6.5/10) Question: Suppose " 0 < X < pi/2 " and " sin X = 5/11 ". Evaluate "cos X" . Express your answer as a fraction.
Click here to see answer by stanbon(57984)

Question 281079: (tough) suppose " pi/2 < 0 < pi " and " sin X = 5/16 "... Evaluate "cos X"
Click here to see answer by Fombitz(13828)

Question 281080: Find the four smallest positive numbers "X" such that cos X = 1
Click here to see answer by Alan3354(31538)

Question 281505: I need to find the exact value of this expression using fundamental identities or the Complementary Angle Theorem. I thought maybe the Complementary Angle Theorem would help but I am not sure how. Thank you for any help. :) By the way, both cosines are squared but when I preview, it does not look like they show up.
Click here to see answer by stanbon(57984)

Question 281579: a stone is thrown vertically upwards at a speed of 24 m/s. its height h meters after t seconds is given approximately by the formula h=24t-5t squared. Use this formula to find when the stone is 27 meters up, and explain the double answer.

apply thr quadratic formula
could someone please help?
Click here to see answer by solver91311(17077)

Question 281690: Find all points [r, theta] of intersection r=1 and r= 2sin(theta)
Multiple choice:
a)[1/2, pi/3] & [1/2, 5pi/3]
b) [1/2, pi/6] and [1/2, 5pi/6]
c) [1, pi/3] & [1,5pi/3]
d) [1, pi/6] and [1,5pi/6]
e) None of these
I want to eliminate A & B because their r-values are 1/2 instead of 1.
If I graph these in Polar mode (in radian mode too), the two graphs form two ellipses. If I trace, I can find intersections at theta = .5236 (pi/6) and 2.618 (5pi/6). So I'm leading toward D as my answer.
First, is it okay to use the graphical approach to solving this problem?
Second, what is the algebraic approach to solving this problem?
Click here to see answer by jim_thompson5910(28717)

Question 281969: verify that Cos^2x*cscx*secx = cotx
Click here to see answer by stanbon(57984)

Question 281968: verify that Cosx (secx+cosx csc^2x) = csc^2
Click here to see answer by Alan3354(31538)

Question 282120: show that cos(3x)/cos(x)=cos^2(x)-3sin^2(x)
Click here to see answer by Edwin McCravy(8999)

Question 282127: find the exact value of sin(arctan(3/4)-2arcsin(2/3)). I managed to get to sin(-7sqrt(5)/5) and i am stuck on what to do after that.
Click here to see answer by Edwin McCravy(8999)

Question 282124: show that 1+cos(x)/sin(x)=sin(x)/1-cos(x)
Click here to see answer by dabanfield(803)

Question 282271: In a triangle ABC, angle B's measurement is 3 times angle A's measurement, and angle C's measurement is 4 degrees less than 6 times angle A's measurement. If a triangle measures 180 degrees all together, what is the measurement of angle A?
Click here to see answer by mananth(12270)

Question 282248: A ramp at a loading dock is placed so that the end of the ramp is 42 ft from the base of the dock and the angle of elevation of the dock is 35 degrees. How long is the ramp. Round to the nearest tenth.
Click here to see answer by nyc_function(2733)

Question 282252: this is my problem that i cannot solve.. sin^4 - cos^4 = 2sin^2 - 1
we can only work on one side of the problem.
this is what i have got so far
(sin^2 + cos^2) (sin^2 - cos^2)=
1(sin^2 - cos^2)=
sin^2 - cos^2
I'm not sure what to do from there to make it equal 2sin^2 - 1
Click here to see answer by mananth(12270)

Question 282266: I also need help on this trig. identity as well.
sin^2 - 1 = -cos^2
Once again thanks! Oh and we are only allowed to change one side of the identity.
Click here to see answer by jim_thompson5910(28717)

Question 282257: this problem also has got me stuck sin(csc - sin)= cos^2
What I worked out, I ended up with a -sin^2 and I don't think that is correct.
Click here to see answer by jim_thompson5910(28717)

Question 282268: This trig. identity is also hard. Can you help me equal it? We are only allowed to work on one side of the problem.
cos/sec + sin/csc = sec^2 - tan^2
Click here to see answer by xachu4u(10)

Question 282269: I need to equal this trig. identity 1/1 -sin = sec^2 + sec(tan)
Click here to see answer by xachu4u(10)

Question 282403: how do you figure out f(3.14) = tan (x/4) + sin (x) ? I have the answer but I don't understand how to figure it out. I keep getting it wrong.
Click here to see answer by nabla(475)

Question 282480:
x^2 - 3x +7 = 0
Find the exact solution.
I have to use the quadratic formula.
could someone explain how to do this?
Click here to see answer by checkley77(12569)

Question 282489:
The vertex of the function
f(x) = x^2 + 6x +7
Click here to see answer by user_dude2008(1861)

Question 282488: if you are standing 85 ft. from the base of a flagpole,and determine that at ground level,you would need to look up at a 30° angle to see the top of the flagpole,how tall is the flagpole. Round the height to tenths.
Click here to see answer by dabanfield(803)

Question 282656: Can you please help me verify the identity.
(sinx-cosx/sinx)+(cosx-sinx/cosx)=2-secx cscx
Thank you so much
Click here to see answer by Alan3354(31538)

Question 282651: Can I please have help with verifying the identity.
sec(x)-1/sec(x)=sin(x)tan(x)

Thank you so much
Click here to see answer by Alan3354(31538)

Question 282663: Solve the equation 4sin(2theta)-3cos=0 for all values on the interval . Express any non-integer answers to the nearest tenth of a degree.
Click here to see answer by Edwin McCravy(8999)

Question 282667: Solve the equation 5cos(2a)+3=0 for all values of a on the interval 0
Click here to see answer by Theo(3504)

Question 282781: Two forces of 40lbs and 20lbs on an object. The angle is 40 degrees between them. What is the angle between the Resultant force and the larger force?
Click here to see answer by Edwin McCravy(8999)

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, 9541..9585, 9586..9630, 9631..9675, 9676..9720, 9721..9765, 9766..9810