Basic Math question and answers for March 19, 2024
- Q Evaluate the expression.sin240 - cos 180 + tan 60=____(Simplify your answer, including any radicals. Use integers
- Q If ?-4+?8+16 cosec ? + sin ? = (5?3)/6 , where ? lies in 1st quadrant, then tan?/2 equals(1) ?6(2) ?3(3)1/(2?3)(4)1/?3
- Q Find all the complex cube roots of w = 8( cos 210 + i sin 210). Write the roots in polar form with 0 in degrees.
- Q Write the following complex number in rectangular form.14( cos 135+ i sin 135)
- Q Sketch a graph that shows at least one full period. Fill in the table of the "five important points" using the method shown in the notes:y=-1+cos [2(x-?/4)]
- Q Use the given conditions.cos(u) = 5/13, 0<u<?/2(a) Determine the quadrant in which u/2 lies.Quadrant IQuadrant IIQuadrant IIIQuadrant IV(b) Find the exact values of sin(u/2), cos(u/2), and tan(u/2) using the half-angle...
- Q Convert the polar equation r (25cos? + 4sin?) =100 to a rectangular equation.
- Q The function graphed to the right is of the form y = a sec bx + c or y = a csc bx + c for some a ? 0,...
- Q Given the equation y = 3+2sin(2x-?) Identify the following: 1) amplitude, 2) period 3) phase shift and 4) give the coordinates of at least 5 key points.Amplitude = Period =
- Q Convert the Cartesian coordinate (-3,-3) to polar coordinates, 0? ? < 2?, r> 0r=Enter exact value.?=
- Q The domain of both the sine and cosine functions is ___, and the range is ____.(Type your answers in interval notation. Type exact answers, using ? as needed.)
- Q Find all real numbers that satisfy the equation. Round approximate answers to the nearest hundredth.2 sin(?x) =Group of answer choices{x|x = 0.33 + 2k or x = 0.67 + 2k}{x|x...
- Q [11] Solve for the variable over C. Circle answers in r cis ? form.-168 + 3x = 2019
- Q Find all solutions of the equation in the interval [0, 2?). (Enter your answers as a comma-separated list. If there is no solution, enter NO SOLUTION.)4 cos x + 4...
- Q An equivalent expression to cos(? ) tan(? ) is:a) sin(?)b)1/cos (? )c) 2 sin(?) cos(?)d) tan(? )
- Q For which of the following is there no solution for x?a) sin(x) - 3 = 0b) sin(x) = 0.5c) sin(x) = -0.5d) sin(x) - 1 = 0
- Q A function of the form f(x) = cos(x) + c passes through the point A(?/3, 1). Thefunction is:a) f(x) = cos(x) +0.5b) f(x) = cos(x) + 1c) f(x) = cos(x)...
- Q In a small fishing village outside of St. John's, Newfoundland, the tides can be modeled by the function: H(t) = 2.5 cos 2?(t - 3)/12 + 4 With H(t) measured...
- Q To calculate the height of a tower Mary measures the angle of elevation from a point A, to be 100. She then walks directly towards the tower, and finds the...
- Q Amy is flying a plane at an altitude of 1150 feet and sees a cornfield at an angle of depression of30. What is the plane's approximate horizontal distance to the...
- Q Prove the following trig identities. Show all of your steps for full marks.a) sec ?cos ? + sec ? sin? = 1 + tan ? b) sin x +sin x...
- Q Using the Law of Sines to solve the all possible triangles if A -If no answer exists, enter DNE for all answers.ZB is 31xdegreesZC is 29x degreesC = 18120, a32,...
- Q Prove the identity.=-cscx - sinx = cotx cosx
- Q Use the product-to-sum identities to rewrite the following expression as a sum or difference.4sin (3?/4) cos (3?/4)
- Q Use the sum and difference identities to determine the exact value of the following expression. If the answer is undefined, write DNE.sin 165 cos75 - cos165 sin75
- Q for sin 2x + Cas x = 0, Use a double angle orhalf angle formula to simplify the equationand then find all solutions of equationin interval [0, 2?).x? =x2=X3
- Q Solve sin(4x) cos(9x) - cos(6x) sin(9x) = -0.45 for the smallest positive solution. X =
- Q Solve 5 sin(2x) +1 cos(x) =D for all solutions 0?x? 2?
- Q Q: The range of the function f(x) = log?13,(5 sin ( (?/3)+ x) +12 sin ((5?/6)+x))) isa) (0,2]b) (-?, 2]c) (-?, 1/2]d) (0, 1/2]
- Q A solution of the first order differential equationy'cos(x+y)+ sin(x+y)/x=e^x-cos(x + y) is(a) sin(x + y)- e^x = constant(b) e^xxtan(x + y) = constant(c) x(cos(x + y)-e^x) + e^x = constant(d)...
- Q Solve for t, 0 < t < 2?.27 sin(t) cos(t) = -9 cos(t)I
- Q Solve 2 cos (w) + cos(w) - 1 = 0 for all solutions 0 ?w < 2.<W=Give your answers as exact values in a list separated by commas.
- Q Graph two periods of the given tangent function. (x- ? / 14 ) y = tan Choose the correct graph of two periods of y= tan ( x- ? /...
- Q A boat leaves the entrance to a harbor and travels 175 miles on a bearing of N 54 E. How many miles north and how many miles east from the...
- Q Use the trigonometric function values of the quadrantal angles to evaluate(sin 90) +8( tan 0) +5 cos 180(sin 90) + 8( tan 0) +5 cos 180 =(Simplify your answer, including...
- Q Find all solutions to the equation.4sint-4cost=4Find all solutions to the equation.4sin t+2sint=2
- Q Verify the identity.sec ?(1-sin ?) = 1To verify the identity, start with the more complicated side and transform it to look like the other side. Choose the correct transformations and...
- Q Rewrite sin (x +7?/4) in terms of sin(x) and cos(x).
- Q The bearing from A to C is S61 E The bearing from A to B is N 87 E. The bearing from B to C is S 29 W A...
- Q The trend of covid cases in Ontario seems to be a neverending sinusoidal function of ups and downs. If the trend eventually becomes the seasonal flu over a 12-month period,...
- Q Simplify sin (t) + cos (t) / cos (t) to an expression involving a single trig function with no fractions.
- Q 2. Test for symmetry and graph the following equation:r=3 sin 2?/sin ? + cos^3 ?
- Q 7. For the given function, state the amplitude and the maximum output for the function:f(t) = 2sin(t)The amplitude is 4 and the maximum value is y = 2.The amplitude is...
- Q Give the exact value of the expression without using a calculator.cos (tan-(-8))
- Q Sketch the graph the function y = csc(22) over the interval [0, ?). Label the x and y-axis so that the important characteristics of the graph are illustrated clearly.
- Q solve sin(x) = -0.54 on 0<x<2?A =B =Give answer accurate to 3 decimalplaces
- Q solve 4sin(4x) = 4 for smallestpositive solutions A and Bwith A<BA =B =Give answer accurate to twodecimal places
- Q Give the equation y=4sin(5?x/4-25?/4)+8Amplitude=Period=horizontal shift =Midline is y=
- Q Show directly that the given functions are linearly dependent on the real line. That is, find a nontrivial linear combination of the following functions that vanishes identicallyf(x)=23, g(x)=5 sin^2x, h(x)...
- Q Find all solutions of the equation. 2 cos x-1=0
- Q A bicycle wheel has radius R. Let P be a point on the spoke of a wheel at a distance d from the center of the wheel. The wheel begins...
- Q A hot-air balloon is rising vertically 14 ft/sec while the wind is blowing horizontally at 4 ft/sec. Find the speed v of the balloon and the angle 8 it makes...
- Q Solve 3 cos(x) - 11 cos(x) - 4 = 0 for all solutions 0 < x < 2?
- Q Solve sin (3x) cos(5x) - cos(3x) sin(5x)=-0.35 for the smallest positive solution.x=
- Q Solve 6 sin(?/3 x) =4 for the four smallest positive solutions
- Q Solve sec(4x) - 8 = 0 for the four smallest positive solutionsx=Give your answers accurate to at least two decimal places, as a list separated by commas
- Q Solve sin (t) = 8 cos(t) for all solutions 0 < t < 2?t =
- Q Find c if a = 2.18 mi, b = 3.45 mi and angle C = 40.2 degrees.Enter c rounded to 3 decimal places.C=Assume angle A is opposite side a, angle...
- Q Simplifysec(t) - cos(t)/ sin(t). to a single trig function with no fractions.
- Q Write the sum as a product:cos(17.6t) + cos(11.2t) =
- Q Solve 8 sin(4x) = 4 for all solutions in the interval (0, 2pi). Give your answers accurate to at least twodecimal places.
- Q Find the value of the given trigonometric function by finding the reference angle a and attaching the proper sign.tan 306
- Q What is the amplitude of the following function? y = 0.379 cos x
- Q Find the horizontal shift.y = sin(4? - pi/2)
- Q A sine function has an amplitude of 4, period of 2?, horizontal shift of -3?,, and vertical shift of 1. What is the y-value of the positive function at x...
- Q Express the following as a function of a single angle.sin 340 cos 120 - cos 340 sin 120sin[?]
- Q A sound wave has an equation y = 7 sin(58?t) where t = time in seconds What is its frequency? [?] cycles/second
- Q 13 Dimensions of a Mirror A person standing 150 centimeters from a mirror notices that the angle of depression from his eyes to the bottom of the mirror is 12...
- Q PART A 1 2 3 4 5 6 7 9 10 11 12 MULTIPLE CHOICE What is the radius of a circle with the equation of x2 y 64 a...
- Q 3 a Dilation of about point M 7 5 M N M 9 8 7 5 N Center to M N 9 8 6 y Center to P O Center...
- Q A 12m tall flagpole was installed in the park A long cable is tied to the top and secured to the ground The angle the cable makes with the ground...
- Q Vome Alice At the local garden shop a package of flower seeds costs 5 and trees costs 17 The gardener purchased 500 items and the total cost is 5 968...
- Q sin 0 11 cos 0 tan 8 csc 8 sec 0 cot 0 values of the six trigonometric functions of the angle 8 shown in the figure 12 13 13...
- Q A buoy floating in the ocean is bobbing in simple harmonic motion with period 8 seconds and amplitude 4 ft Its displacement from sea level at time t 0 seconds...
- Q Match each angle in Column I with its reference angle in Column II 45 37 31 83 60 30 Drag each reference angle above to the corresponding angle below Answers...
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