Basic Math question and answers for October 11, 2024
- Q Given a right triangle with sin(?) = 6/11, determine the value of the other trigonometric ratios of ?.1. cos(?)2 tan(?)=3. sec(?)4. csc (?) =5. cot(?)=Use exact notation, no decimal approximations.If...
- Q For each angle (in radians) below, determine the quadrant in which the terminal side of the angle is found.[NOTE: Enter '1' for quadrant I, '2' for quadrant II, '3' for...
- Q Consider the function y = 3 cos8In the "Show Work" area:(a) Determine the amplitude and period.(b) Using by-hand techniques, determine the 5 key points of the first cycle.(c) Sketch exactly...
- Q For a project in his Geometry class, Ajay uses a mirror on the ground to measure the height of his school's football goalpost. He walks a distance of 8.85 meters...
- Q Solve for exact solutions over the interval [0,360).cos ?/2 = -1/2Select the correct choice below and, if necessary, fill in the answer box to complete your choice.A. The solution set...
- Q 3A 25-foot water slide has a 10.8-ft ladder which meets the slide at a 100 angle. To the nearest tenth, what is the distance between the end of the slideand...
- Q 5Two observers are 2.4 miles apart on opposite sides of a hot-air balloon. The angle of elevation from observer A is 30 and the angle of elevation fromobserver B is...
- Q If line segment AB = 15 and ?B = 62, find line segment AC. Round to the nearest tenth. 11.6 13.2 13.7 12.6
- Q Use the law of sines to solve the given problem.The loading ramp at a delivery service is 11.5 ft long and makes a 20.0 angle with the horizontal. If it...
- Q Find the principal root of this equation:tan(x) = -1
- Q Determine one positive and one negative coterminal angle for the angle given.60 15'Choose the correct answer below.A. 24015'; -20945'B. 42015'; -29945'C. 24015'; -11945'D. 42015'; -11945'E. 33015'; -29945'F. 33015'; - 20945'
- Q 2x2 - 2y2 = 2x + yWhich of the following gives the polar form of the equation above?
- Q If 2sin?+ 6 = -?3+6, where 0 ? ? < 2?, what are the values of ??Enter your answer(s) in radians. If necessary, separate multiple values by commas.Provide your answer...
- Q Which of the following is equivalent to csc acsc sin (a + B) for all values of a and B for which csc acsc sin (a + B) is defined?Select...
- Q You are given that cos(A) =-5/13 with A in Quadrant III, and cos(B) =8/17 with B in Quadrant I. Find cos(A + B).Give your answer as a fraction.Provide your answer...
- Q Find the exact value of the expression given below.COS (?/12)
- Q Find the exact value of the expression given below.cos(15)....cos(15%) =(Simplify your answer, including any radicals. Use integers or fractions for any numbers in the expression. Rationalize all denominators.)
- Q Evaluate the following expression with a calculator.arccot (-3.5)Express your answer in degrees, and round to the nearest hundredth.Hint: Make sure your answer is within the range of the arccot function.Provide...
- Q Write the function value in terms of the cofunction of a complementary angle.sin 61
- Q Which of the following is equivalent to sin(-3) tan csc cot 3 for all values of 3 for which sin(-6) tan 6 csc cot Bisdefined?Select the correct answer below:0 1O-1O...
- Q Which of the following is equivalent to csc ?(sec ?- 1) (sec ? + 1) for all values of ? for whichcsc ?(sec ?-1) (sec ? + 1) is defined?Select...
- Q Find the exact value of the expression given below.cos(105)Rewrite the expression using a sum or difference formula. Choose the correct answer below.A. cos(105) = cos (60 +45) = sin (60)...
- Q First, determine the quadrant for ?, then find x, y, and r; and finally, give all six trigonometric ratios for ? given the following information:tan(?) = 2/9 and cos(?) <...
- Q Considering only the values of 3 for which the expression is defined, which of the following is equivalent to the expression below? cos(-?).tan?.csc(-?).sec(-?)
- Q Given sin(A) =1/3 with A in quadrant II and cos(B) = -5/9 with B in quadrant III. Solve for sin(A + B), and cos(A + B) and tan(A + B)....
- Q Determine the exact values of sin and cosgiven that the terminal side of angleintersects4the unit circle in the first quadrant at (y).15Provide your answer below:sin = 050==COS
- Q Verify that the following equation is an identity.sin 12a=4 sin 3a cos 3a cos 6aTo verify the identity, start with the more complicated side and transform it to look like...
- Q If f(x) = 3sin-x-2cos-x, then f(x) is(A) even function(C) neither even nor odd(B) odd function(D) even as well as odd function.
- Q Consider the generalized cosine function: f(x) = A cos(B(x - h)) + k.(a) What is the period of f(x)?(b) What is the midline of the function f(x)? y =(c) What...
- Q Venly that the following equation is an identity.sin 12? =4 sin 3? cos 3? cos 6?
- Q What's a radian?A) The ratio between a circle's circumference and its radiusB) The ratio between a circle's diameter and its radiusC)An angle made at the center of a circle by...
- Q Find the mid points between the x-intercept and each of the vertical asymptotes ofthe function y = 5/2tan(2x)
- Q Solve the following equation on the interval [0, 360). Round answers to the nearest tenth. If there is no solution, indicate "No Solution."- 10sin(x) = -4csc(x) - 3
- Q Use appropriate Identities to rewrite the following expression in terms containing only first powers of sine.-8tanx1+tan2x
- Q A 13-ft ladder is leaning against a house when its base starts to slide away. By the time the base is 12ft from the house, the base is moving at...
- Q Use trigonometric Identities to simplify the expression.1/cot(x)tan(-x)
- Q Consider the function y = - 4 cos (2x). In the "Show Work" area:(a) Determine the amplitude and period.(b) Identify the 5 key points of the first cycle.(c) Then, sketch...
- Q A customer brings a special window frame, shown in the following diagram, to a glass shop. The wood frame has inside dimensions FG = 80 cm and HF = 136...
- Q Analyze and sketch a graph of the function. Identify any relative extrema, points of inflection, and asymptotes. Use a graphing utility to verify your results.f(x) = arcsec(2x)maximum (x, y) =minimum...
- Q Fvideonswer:(Diagram is not to scale.)Edulastic: Formati... ClassesOlivia is 1.25 meters tall. At 3 p.m., she measures the length of a tree's shadow to be32.25 meters. She stands 28.1 meters away...
- Q Find the radian measure of the arc of a sector that has a sector area of72? and the area of the circle is 360?. Leave your answer in terms of...
- Q Verify that the equation is an identity.tana + 1/(sec ?)= sec ?To verify the identity, start with the more complicated side and transform it to look like the other side....
- Q (1) Rewrite the trigonometric function in terms of reference angle (do not evaluate):(3)-0cot(2) Using the above, evaluate the exact value of the trigonometric function:cotot (-3)=0Note: Decimals are NOT allowed in...
- Q Determine the exact value of two trig functions of a given angle (one in degrees and one in radians) by drawing a picture of each given angle in standard position,...
- Q Henry is riding a Ferris wheel at a carnival. After a time t, his height H above the ground is given by the following formula. H=a cos (bt)+c Find Henry's...
- Q Use a cofunction to write an expression equal to csc 72.
- Q Prove the identity.sinx- -sin4x= cosx-cos4xNote that each Statement must be based on a Rule chosen from the Rule menu. To see a detaselect the More Information Button to the right...
- Q Use the quadratic formula to solve for x.2x-8x=1Round your answer to the nearest hundredth.If there is more than one solution, separate them with commas.
- Q Prove the identity.cotx (secx-1)=1Note that each Statement must be based on a Rule chosen from the Rule menu. the right of the Rule.
- Q Use a cofunction to write an expression equal to tan ?/7
- Q In studies of fluid mechanics, the equationY?V? sin(a) = 72V2 sin(a - B),where 1, 2, V1, V? are constants, sometimes arises. Show that if y1 V? = 72V2, the equation...
- Q If cos(?)= 1/5 and is in the 4th quadrant, find the exact value for sin (?)
- Q If ?=5?/6, thensin (?) =cos(?) =Give exact values. No decimals allowed!
- Q A rope with a Ingth of 3.5 meters is tied from a stake in the ground to the top of a tent. It forms a 17 degree angle with the...
- Q Consider the function y = 5 cos (2x). In the "Show Work" area:(a) Determine the amplitude and period.(b) Identify the 5 key points of the first cycle.(c) Then, sketch the...
- Q In 1-6, match each statement with the correct value.Drag each of the values given above into the appropriate area to match the descriptions below.1. The least positive value k for...
- Q Graph the curve given below over the given interval, together with its tangents at the given values of x. Label each curve and tangent..y = sec x,-?/2<x<?/2,x=-?/3,?/4What is the equation...
- Q A 20-meter line is used to tether a helium-filled balloon. Because of a breeze, the line makes an angle of approximately 85 with the ground. Use a trigonometric function to...
- Q A ramp is propped against the back of a truck. There is a 30 degreeangle between the ramp and the horizontal pavement.If the distance along the ground from the end...
- Q When working in two-point geometric perspective, artists must scale their work to fit on the paper or canvas they are using. In doing so the expression A/B arises, where A...
- Q A surveyor needs to determine the distance between two points that lie on opposite banks of a river. Two points, A and C, along one bank are 250 yards apart....
- Q Use a power-reducing identity to rewrite the following expression below in terms containing only first powers of cosine.cos6(x)
- Q The Unit Circle gives exact values of trig functions at special angles. When the angle is not one of the special angles, we may sometimes use the Summation Identities and...
- Q A particular curve is represented parametrically byx = -5 cos 2t, y = 6 sin 21, t ? [0, ?/2].(a) As t increases on [0, ?/2], in which direction is...
- Q A person who is 1.65m high, stands 25.7m from the base of a building. She looks up atthe top of a near building at an angle of elevation of 35.4.a)...
- Q Given that sec(?)=?10 and ? is in Quadrant IV, what is tan(?)?Select the correct answer below:?10/3-?10/31/33-3-1/3
- Q A camper wants to protect her bag of food from bears. She decides to tightly stretch a ropebetween two trees and hang her bag from a point exactly halfway along...
- Q A 24-foot ladder rests against a house near a second story window 20 feet from the ground. Assume that the ladder and the house both sit on level ground.To the...
- Q The top of a 22-foot ladder rests against the top of an 18-foot wall. If the base of the ladder is on the same ground level as that of wall,...
- Q As shown in the diagram, a ship sails 16 nautical miles east from a harbor. It then sails 18 nautical miles in the direction ofN 55 E. How far is...
- Q A 10-foot ramp must make an angle of 30 with the ground if it is to reach a certain window. What angle must a 15-footramp make with the ground to...
- Q Solve the equation on the interval 0 ??<2?.sin(2?) =What are the solutions to sin (2) =
- Q Solve the equation. Give a general formula for all the solutions. List six solutions.cos?= 0Write the general form for all the solutions to cos 0 = 0 based on the...
- Q Suppose that the point (-1,- 6) lies on the terminal side of an angle 0. Enter the exact values of thetrig functions below:cos(0) =cot (0) =tan(0) =csc (0)sec (0) =sin(0)...
- Q Part A: Given sin?=?3/2 , determine three possible angles ? on the domain [0,?). Part B: Given ? = 675, convert the value of ? to radians and find sec...
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