# Questions on Algebra: Trigonometry answered by real tutors!

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 Algebra: Trigonometry Solvers Lessons Answers archive Quiz In Depth

 Question 38968: without using a calculator or a table, find the value of each expression. leave your answers in terms of pi whenever appropriate. a. inverse tan of 1 b. inverse sin of sqrt 3/2 c.invers cos (-sqrt 3/2) d.inverse tan sqrt 3 e.inverse sin of 0 f. sin(inverse cos 3/5) g. sec(inverse tan 5/12) h. cos(inverse sin of 1) Click here to see answer by venugopalramana(3286)

 Question 39280: what is the period of the function y=sin(x/4)? Click here to see answer by fractalier(2101)

 Question 39283: what is the amplitude, period, phase shift, and vertical displacement for y= (square root 7)cos[5(x-85 degrees)] - 1.2 Click here to see answer by fractalier(2101)

 Question 39356: Solve for all values of x if x is measured in degrees. 2cos^2x=3sinx 2(1-sin^2x)=3sinx 2-2sin^2x=3sinx 2sin^2x+3sinx-2=0 (2sinx-1)(sinx+2)=0 sinx=1/2 or sinx=-2 Sinx cannot equal -2 so, sinx=1/2 x=[30 +-n(360)]degrees and x=[(150)+-n(360)degrees] These are all the solutions. Cheers, Stan H. Thanks for your help! Click here to see answer by stanbon(57222)

 Question 39543: why should we take sin theta as opposite/hypotenuse is there any proof for it can u please send it to me on my email address Click here to see answer by fractalier(2101)

 Question 36996: Factor the expression sec^2t + 5 sec t + 6 Factor the expression tan^2t - 3 tan t + 10 Click here to see answer by venugopalramana(3286)

 Question 39644: what is the exact value of 6cos(-61pie/6) - 2sin(13pie/4) Click here to see answer by venugopalramana(3286)

 Question 37066: (1) find the exact value of sec(225degrees) (2) In the triangle ABC, find A, if B= 100 degrees, and a=20. (3) In the triangle ABC, find b, iF A=15, C=12 and angle b=150 degrees. Click here to see answer by venugopalramana(3286)

 Question 40418: for what values of x is the expression (sin^(3)x-cos^(3)x)/tan(^3)x undefined? Answer: 2kπ where k is an arbitrary integer why? thank you. Click here to see answer by venugopalramana(3286)

 Question 40416: S and T are the centers of their respective circles. The two circles are mutually tangent at point U. If segment RS = d, what is the radius of the smaller circle in terms of d and ? Answer: d(cos – sin ) solution? thank you Click here to see answer by venugopalramana(3286)

 Question 40414: i-ABC is an acute triangle ii-ABC is an isosceles traingle iii-ABC is an obtuse triangle where B is an obtuse angle iv-ABC is a right triangle where A is the right angle v-ABC is an obtuse triagnle where A is the obtuse angle In a triangle ABC, sinA < a/c and cosA > b/c. How many of the above statements are always false regarding triangle ABC? Answer.3 why? Click here to see answer by AnlytcPhil(1276)

 Question 40524: solve sin2y = cos4y for y, where 0 degrees < or equal to y < 360 Click here to see answer by josmiceli(9649)

 Question 40525: the sun rises at 09:17 on dec. 21 and at 04:35 on June 22> there is no daylight savings time, the time the sun rises on any other date can be predicted from a sinusoidal grpah with period of 365 days. Write a sinusoidal equation that relates the time the sun rises to the day of the year Click here to see answer by AnlytcPhil(1276)

 Question 40540: The vector v has an initial point P and terminal point Q. Write v in the form ai+bj; that is, find its positive vector. P=(-2,-1);Q=(6,-2) Click here to see answer by stanbon(57222)

 Question 40539: The vector V has initial point P and terminal point Q. Write V in the form ai+bj; that is find its positive vector. P=(0,0);Q=(3,4) Click here to see answer by longjonsilver(2297)

 Question 40533: Can you please check my answer? Our professor has shown us how to get these answers in decimal, and the book shows how to get them with radicals. Question: A child pulls a wagon with a force of 40 lbs. The handle of the wagon makes a angle of 30° with the ground. Express the force vector F in terms i and j. Answer: 17.32i+10j Thank You Click here to see answer by longjonsilver(2297)

 Question 40738: A guy wire (a type of support used for example, on radio antennas) is attached to the top of a 50 foot pole and stretched to a point that is d feet from the bottom of the pole. Express the angle of inclination as a function of d. Click here to see answer by stanbon(57222)

 Question 40733: A lobster boat is situated due west of a lighthouse. A barge is 12 km south of the lobster boat. From the barge the bearing to the lighthouse is 63 degrees (12 km is the length of the side adjacent to the 63 degree bearing). How far is the lobster boat from the light house? Click here to see answer by Paul(988)

 Question 40734: A recent land survey was conducted on a vacant lot where a commercial building is to be erected. The plans for the future building construction call for a building having a roof supported by two sets of beams. The beams in the front are 8 feet high and the back beams are 6.5 feet high. The distance between the front and back beams is 8 feet. At what angle will the roof lay on the front beam? Click here to see answer by rajagopalan(158)

 Question 40736: Latitude presents special mathematical considerations for cartographers. Latitude is the north-south location on the earth between the equator and the poles. Since the earth flattens slightly at the poles, a nautical mile varies with latitude. A nautical mile is given by N(e) = 6066 - 31 * cosine 2e. e represents the latitude in degrees. •What is the length of a British nautical mile at Chicago (latitude of 42 degrees)? •What is the length of a British nautical mile at the North Pole (latitude of 90 degrees)? •Express N(e) in terms of cosine e only, do not use the double angle. •At what latitude north is the length of a British nautical mile found to be 6040 feet? Click here to see answer by longjonsilver(2297)

 Question 40819: Draw a right angled triangle ABC with vertical side AB, horizontal side BC and . Let angle ACB = x degrees Given: and AB = 11 ft To find: BC Note, or BC = = 55 ft Thus the horizontal run must be 55 ft long. Click here to see answer by psbhowmick(529)

 Question 40903: I need help...here is my question and the start to my answer...please help (Q) Two cars with new tires are driven at an average speed of 60 mph for a test drive of 2000 miles. The diameter of the wheels of one car is 15 inches. The diameter of the wheels of the other car is 16 inches. If the tires are equally durable and differ only by diameter, which car will probably need new tires first? Why? (A) The formula for circumference is 2 * pi * radius ( or pi * diameter) So the circumference for the 16 in tire would be 16*pi = 50.26 The circumference of the 16 in. tire is : 16 * pi = 50.26 In 2000 miles, the 16 in. tire has rotated 2000/50.26 = 39.79 times So, the 16 in. tire has done more work. Click here to see answer by Nate(3500)
 Question 40903: I need help...here is my question and the start to my answer...please help (Q) Two cars with new tires are driven at an average speed of 60 mph for a test drive of 2000 miles. The diameter of the wheels of one car is 15 inches. The diameter of the wheels of the other car is 16 inches. If the tires are equally durable and differ only by diameter, which car will probably need new tires first? Why? (A) The formula for circumference is 2 * pi * radius ( or pi * diameter) So the circumference for the 16 in tire would be 16*pi = 50.26 The circumference of the 16 in. tire is : 16 * pi = 50.26 In 2000 miles, the 16 in. tire has rotated 2000/50.26 = 39.79 times So, the 16 in. tire has done more work. Click here to see answer by checkley71(8403)

 Question 40904: Please help.... Explain why tan(x + 450 degrees) cannot be simplified using the tangent sum formulas, but can be simplified by using the sine and cosine formulas. Give examples. I do know that Tan(x+450)cannot be simplified using the tangent sum formula because it cannot be divided by zero. Click here to see answer by fractalier(2101)

 Question 40967: If log sin x = a and log cos x = b, then log (cot ^2 x + 1) = ? Click here to see answer by fractalier(2101)

 Question 41491: can someone please help me understand when an elimination method for solving a system of equations would be preferable over the substitution method? Thank you Click here to see answer by stanbon(57222)

 Question 41495: Please help! In mountain communities, helicopters drop chemical retardants over areas which approximate the shape of an isosceles triangle having a vertex angle of 38 degrees. The angle is included by two sides, each measuring 20 ft. Find the area covered by the chemical retardant. Click here to see answer by Nate(3500)

 Question 41592: simplify these expressions: (2cotB)/(1+cot^B) the answer is supposed to be 2cosBsinB but i have no idea how that occurs. Click here to see answer by AnlytcPhil(1276)

 Question 41497: Please help! The chemical retardants are freight shipped from a warehouse. A shipping crate that weights 450 kilograms is placed on a loading ramp that makes an angle of 30 degrees with the horizontal. Find the magnitude of the components of the crate's weight perpendicular and parallel to the incline. Click here to see answer by Paul(988)

 Question 41892: Please Help...I am clueless The meteorologists at the National Interagency Fire Center had pizza delivered to their operations center. Their lunch consisted of pizza, milk and gelatin. One slice of cheese pizza contains 290 calories, 15g of protein, 9g of fat, and 39g of carbohydrates. One-half cup of gelatin dessert contains 70 calories, 2g of protein, 0g of fat, and 17g of carbohydrates. One cup of whole milk contains 150 calories, 8g of protein, 8g of fat, and 11g of carbohydrates. Write 1 x 4 matrices P, G, and M that represent the nutritional values of each food. Find 3P+2G+2M and tell what the entries represent. Click here to see answer by longjonsilver(2297)

 Question 38729: A sine wave test generator is an electronics labaratory can deliver two sine signals to a prototype electronic circuit. The equations for the sine wave signals are known to be Y1=4 sin^2 x+5 and y2 = 8 - sin x find all values of x in degrees for which the two sine wave signals meet in the interval 0 deg greater or equal x less than 360 deg. (algebraic equation) Click here to see answer by fractalier(2101)

 Question 41967: Graph the following: y= sin 2 [x+ Pie divided by 2]+3 Click here to see answer by psbhowmick(529)

 Question 41984: (cos250*cos25) + (sin250*sin25) a.k.a. (the cosine of 250 degrees multiplied by the cosine of 25 degrees) plus (the sine of 250 degrees multiplied by the sine of 25 degrees) Click here to see answer by fractalier(2101)

 Question 41986: (tan(170) - tan(50)) / 1 + tan(170)*tan(50) ((the tangent of 170 degrees) minus (tangent of 50 degrees)) all divided by 1 plus (tangent of 170 degrees multiplied by tangent 50 degrees) Click here to see answer by abcdefg(37)

 Question 41979: tan-1 (– the square root of 3) aka- the angle whose tangent is the negative square root of three the possible answers are A. -30 degrees B. -60 degrees C. 150 degrees D. 120 degrees Click here to see answer by abcdefg(37)

 Question 41980: sin-1(-(the square root of 3)/2) aka the angle whose sine is the (negative (square root of 3) divided by 2) the possible answers are A. -30 degrees B. -60 degrees C. 150 degrees D. 120 degrees Click here to see answer by abcdefg(37)

 Question 41982: (tan(x) + cot(x))/csc2(x) a.k.a. ((the tangent of x) plus (the cotangent of x)) all divided by the cosecant squared of x Click here to see answer by fractalier(2101)

 Question 42273: The edges of a saw tooth are 1.39mm and 3.26mm long. The base of the tooth is 2.05mm long. At what angles do the edges of the tooth meet? Click here to see answer by fractalier(2101)

 Question 42272: An observer measures the angle of evevation to the top of a mountain and obtains a value of 39 degrees. After moving 100m farther away from the mountain,the angle of elevation is massured as 38.2 degrees. How tall is the mountain? Click here to see answer by psbhowmick(529)

 Question 42271: A tower stands vertically on sloping ground whose inclination with the horizontal is 13 degrees. From a point 40.0m downhill from the tower (measured along the slope) the angle of elevation of the top of the tower is 20 degrees. How tall is the tower? Click here to see answer by psbhowmick(529)

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