Basic Math question and answers for March 08, 2024
- Q Convert the polar coordinate (9, ?/3) to Cartesian coordinates. Enter exact values.X =y =
- Q Convert the polar coordinate (7,?/3) to Cartesian coordinates.
- Q Evaluating the sine of a difference of two angles can be done using sin(A - B) = ?a) sin(A) sin(B) - cos(A) cos(B)b) cos(A) cos(B) + sin(A) sin(B)c) cos(A) cos(B)...
- Q Represent the given fraction as a decimal by using the long-division algorithm.3/8
- Q Solve for the variable over C. Circle answers in r cis ? form.x^6 = 64i
- Q Based on the period of f(x)=3sin(2(x-30))-4, how should the horizontal axis of the graphbe scaled?Scale of 45 degrees?Scale of 60 degrees?Or scale of 22.5 degrees?
- Q [6] Polar coordinates of a point are given. Find the rectangular coordinates of each point.Note: If is a "special" angle, then the coordinates should be exact. Otherwise, round to the...
- Q For the function f(x) = -3 sin 5(x -?/6) + 8 the vertical shift is:a) 8 units downb) 5 units upc) 8 units upd) 3 units up
- Q The horizontal distance needed for the graph of a trigonometric function to repeat itself is called the:a) amplitudeb) vertical shiftc) periodd) phase shift
- Q All asymptotes to the function f(x) = csc x occur when:a) cos x = 1b) sin x = 1c) sin x = 0d) cos x = 0
- Q Which expression is equivalent to: 1 - 2 sin(?)a) sin(?)+1b) cos (?) - sin(?)c) 1 - tan (?)d) 2 cos(?)+1
- Q For f(x)=sinx+3 the minimum and maximum values are:a) 3 and 4b) 1 and 2c) 1 and 3d) 2 and 4
- Q The function f(x) = ? tan(x) is an example of a:a) horizontal translation.b) a reflection in both the x-axis and y-axisc) reflection in the y-axisd) reflection in the x-axis
- Q Given sin A =-6/?61 and that angle A is in Quadrant IV, find the exact value of cos A in simplest radical form using a rational denominator.
- Q Find the exact value of sin (7?/12)a) (?3+1)/?2b) (?3-1)/2?2c) (1+?3)/2?2d) (1-?3)/2?2
- Q Find an equivalent expression to cos (x + 3?/2)a) -cos(x)b) sin(x)c) cos(x)d) -sin(x)
- Q Which of the following expressions is equivalent to:1/(1+ sin(?)) + 1/(1-sin(?))a) 2 cos (?)b) 2 sec(?)c) cos (?)d) 2 csc(?)
- Q Which one of the following is not a Pythagorean identity?a) They are all Pythagorean identitiesb) 1- cot (?) = csc(?)c) tan (?) + 1 = sec (? )d) sin (?...
- Q For the function f(x) = -2 cos (3x - ?/2) -1, the phase shift is:a) ?/2 units to the rightb) ?/2 units to the leftc) ?/6 units to the rightd)...
- Q A trigonometric function of the form f(x) = sin x has been transformed to have amaximum at 6.5 and a minimum at 2.5. The equation of the new function would...
- Q An equivalent expression to cot(?) is:a) sec(?) - 1b) csc(?) - 1c) csc(?)+1d) sec(?) + 1
- Q A sine function is reflected in the x-axis and the y-axis. A possible function is:a) f(x) = -sin xb) f(x) = sin x 1c) f(x) = -sin(-x)d) f(x) = sin(-x)
- Q The trigonometric functions have a period of 2? radians. This statement is:a) true for both the sine and cosine functionsb) true only for the sine functionc) true for all three...
- Q The cosecant function has restrictions in its domain that can be expressed as:a) x ? n? where n ? Zb) x ? ? where n ? Zc) x ? ?...
- Q An equivalent expression to cos(-x) is:a) - sin(x)b) cos(x)c) sin(x)d) - cos(x)
- Q Find the exact value of sin ( 7?/4 )a) 1/?2b) 1/?3c) -1/?2d) - 1/?3
- Q Which of the following is an equivalent expression to:(1-cos(?))/(sin(?) cos(?))a) 2 sin(?) cos(?)b) 1/cos(?)c) tan (?)d) 1/sin ?
- Q Find the exact value of cos (5?/12)a) ?3-1/2?2b) 1+?3/?2c) 1-?3/?2d) 1+?3/2?/2
- Q Which of the following is equivalent to:tan (?)/cos(?)a) 1b) sec(?)/cot (0)c) csc (?)/sin(?)d) cos(?)/cot (?)
- Q Find sin 2x, cos2x, and tan 2x if cosx=-3/?10 and x terminates in quadrant II.
- Q Find the exact value of the expressions cos(?+), sin(? + ) and tan(a +) under the following conditions:sin(?) =40/41, x lies in quadrant I, and sin(?) =12/13 lies in quadrant...
- Q Verify the following identity. sin x + cos2x = 1 - sin x To transform the left side into the right side, should be changed to___ and the left side...
- Q A point on the terminal side of an angle ? in standard position is given. Find the exact values of the six trigonometric functions of ?.(-1/3,-1/4)sin ? =cos ? =tan...
- Q Using the Law of Sines to solve the triangle if ?A = 38, ?C = 72, b = 20:?B is___degrees;a=c =Round to two decimal places if needed.Assume ?A is opposite...
- Q Express the given product as a sum or difference containing only sines or cosines.sin (9x) sin (7x)
- Q While working on a geometry problem, Raul determines that the angles of one triangle are congruent to the corresponding angles of another triangle. Which of the following is a valid...
- Q A triangle with side lengths of 5, 12, and 15 centimeters is similar to another triangle. The longest side of the other triangle has length 24 centimeters. What is the...
- Q Graph the trigonometic function. y=-1/2 sin 2x. plot all points corresponding to x- intercepts, minima and maxima within one cycle.
- Q Find all EXACT solutions of the equationcos(x) =-?2/2in the interval [0,2x). If there is more than one answer, enter them in a list separated by commas. Enter an exact expression;...
- Q Which of the following expressions is equivalent to: cos (? ) / 1-sin (?)a) 1+ sin(? )b) 1 + tan (? )c) 1 + cos (?)d) 1+ sin(?)
- Q Find all values of 0 and all values of 0 in [0, 2?] for the equation given below. Be sure to the algebra or trigonometry you use and give exact...
- Q Solve the following equation on the interval[0, 360). Separate multiple answers with a comma. Remember to include a degree symbol.4cosx sinx - sinx = 0
- Q Use trigonometric identities and algebraic methods, as necessary, to solve the following trigonometric equation. Please identify all possible solutions by including all answers in [0, 2?) and indicating the remaining...
- Q Let F= {f|f: R? R} denote the vector space of real-valued functions.Which of the following are linearly independent subsets in F?S = {sin x, cos x}T = {1, sin x,...
- Q Rewrite tan60 in terms of the appropriate cofunction.
- Q Write the sum as a product:.sin(20.1s) - sin(11.1s)
- Q Find cos (u/2) if sin u = - 0.647 and u is in Quadrant-IV.
- Q write product as a sum or difference 4cos (32s) sin(20s)
- Q simplify and write the trig expression in terms of sine and cosine.
- Q Solve 3 sin 2 (w)-13 sin(w) + 4 = 0 for all solutions OLW LIT W = Give answer accurate to 2 decimal Places, as a list seperated by commas.
- Q If sin x = 2/7, x in quadrant 1, then FindSin (2x)cos (2x)tan (2x)
- Q convert the cartesian coordinate (3,-5) to Polar coordinates, 0?0 ? 27.
- Q Two straight roads diverge at an angle of 45. Two cars leave the intersection at 2:00 P.M., one traveling at 42 mi/h and the other at 38 mi/h. How far...
- Q Solve cot(x) = - 7 on 0 ? x < 2?There are two solutions, A and B, with A BA =B =Give your answers accurate to 4 decimal places
- Q Evaluate and round to the forth number after the decimal point.sin 74?cos 48?tan 38?
- Q Prove the following identity: sin(2x) 11 - cos(2x) tan(x)
- Q Write the product as a sum or difference:8 cos(24a) cos(17a) =
- Q Write the sum as a product:cos(22.5p) - cos(3.9p) =
- Q Write the product as a sum or difference:12 sin(28y) sin(12y)=
- Q Verify the identity.cos 0(1+ tan e) = 1To verify the identity, start with the more complicated side and transform it to look like the other side. Choose the correct transformations...
- Q A hot-air balloon is rising vertically. The angle of elevation from a point on level ground 123 feet from the balloon to a point directly under the passenger compartment changes...
- Q Use identities to write each expression in terms of sin ? and cos? FIRST. Then, simplify so that no quotients appear. tan? (1+ cot?)
- Q Solve the equation for solutions over the interval [0,360). (tan ?-1)(cos?-1) = 0
- Q The hypotenuse of a right triangle is 3 less than twice the shorter leg. The length of the other leg is 3 more than the shorter leg. Find the length...
- Q Write the complex number in trigonometric (polar) form. - 4 + 4i?3
- Q An airplane is sighted at the same time by two ground observers who are 3 miles apart and both directly west of the airplane. They report the angles of elevation...
- Q Solve the equation on the interval [0, 2?).sin 2x + sin x = 00,2?/3,?,4?/3?/4,3?/4,5?/4,7?/4?/8,9?/8no solution
- Q Graph the function and y = cos x in the same rectangular system for 0 ? x ? 2?y = 3 cos x
- Q cos ? =2/3 ,tan ?<0 find sin ?-3/2-?5-?5/3-?5/2
- Q cos x + sinx/cosx - sinx-cos/sinxsec x csc X2 + sec x csc X1 - sec x csc X2 - sec x csc X
- Q Complete the identity.sin^2 x + tan^2x + cos^2x = ?sec xtan xcotxsin x
- Q Solve the equation on the interval [0, 2?).cos^ 2 x + 2 cos x + 1 = 0? /2 ,3?/7??/4,7?/42?
- Q From the professor's perspective, explain the pros and cons of using the method below in finding trigonometric values of special angles. Then present an example to illustrate the process. (a)...
- Q Solve for the exact solutions in the interval [0, 2?) . Separate solutions with a comma. If the equation has no solutions, respond with DNE. sin(4x) = 1/ 2
- Q Find the least positive value of ?tan(7?-4) =1/cot(6?+4)
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