Hits: 108
Hits: 108 Question i. Given that and find in terms of . ii. Solve the equation giving all solutions in the interval 0◦ ≤ x ≤ 360◦. Solution i. We are given; We are given that ; therefore; ii. We are required to solve giving all solutions […]
Hits: 137 Question The diagram shows the part of the curve for . i. Use the trapezium rule with 2 intervals to estimate the value of giving your answer correct to 2 decimal places. ii. The line y=x intersects the curve at point P. Use the iterative formula to determine the […]
Hits: 77 Question The curve with equation has one stationary point in the interval . Find the exact x-coordinate of this point. Solution We are required to find the x-coordinate of stationary point of the curve with equation; A stationary point on the curve is the point where gradient of the curve is […]
Hits: 159 Question The diagram shows the curve , for . A rectangle OABC is drawn, where B is the point on the curve with x-coordinate , and A and C are on the axes, as shown. The shaded region R is bounded by the curve and by the lines x = and […]
Hits: 75 Question Solve the equation , for . Solution We are required to solve; Therefore; We have the trigonometric identity; Let , then; Since , therefore; Using calculator we can find that; Properties of Domain Range Periodicity Odd/Even Translation/ Symmetry We utilize the periodicity/symmetry property of to find other solutions (roots): […]
Hits: 134 Question The diagram shows the curve , for . A rectangle OABC is drawn, where B is the point on the curve with x-coordinate , and A and C are on the axes, as shown. The shaded region R is bounded by the curve and by the lines x = and […]
Hits: 76 Question Solve the equation , for . Solution We are required to solve; Therefore; We have the trigonometric identity; Let , then; Since , therefore; Using calculator we can find that; Properties of Domain Range Periodicity Odd/Even Translation/ Symmetry We utilize the periodicity/symmetry property of to find other solutions (roots): […]
Hits: 107 Question (i) Show that (2 sin x + cos x)2 can be written in the form (ii) Hence find the exact value of Solution i. We are given that; We have formula; Therefore; Therefore; Therefore; ii. We are required to find the exact value of; From (i) we […]
Hits: 53 Question i. Given that , find the value of . ii. Hence, showing the use of an appropriate formula in each case, find the exact value of a. b. Solution i. We are given that; We have trigonometric identity; Let , then; Since , therefore; […]
Hits: 156 Question (i) Show that and hence find the exact value of; (ii) The region enclosed by the curve y = tan x + cos x and the lines x = 0, and y = 0 is shown in the diagram. Find the exact volume of the solid produced when this region […]
Hits: 170 Question The diagram shows the curve , for . The x-coordinate of the maximum point M is denoted by . i. Find and show that satisfies the equation tan 2x = 2x + 4. ii. Show by calculation that lies between 0.6 and 0.7. iii. Use the iterative formula to […]
Hits: 93 Question i. Express in the form , where and , Give the value of correct to 2 decimal places. ii.Hence solve the equation for . iii. State the largest value of k for which the equation has any solutions. Solution i. We are given the expression; We are […]
Hits: 147 Question (i) Show that (2 sin x + cos x)2 can be written in the form (ii) Hence find the exact value of Solution i. We are given that; We have formula; Therefore; Therefore; Therefore; ii. We are required to find the exact value of; From […]
Hits: 112 Question i. Given that , find the value of . ii. Hence, showing the use of an appropriate formula in each case, find the exact value of a. b. Solution i. We are given that; We have trigonometric identity; Let , then; Since , therefore; […]