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1 Fig. 8 shows a sketch of part of the curve y=x sin 2x, where x is in radians. The curve crosses the x-axis at the point P. The tangent to the curve at P crosses the y-axis at Q. X P vy=x sin 2x Figh (i) Find Hence show that the x-coordinates of the turning points of the curve satisfy the equa dx tan 2x + 2x = 0. (ii) Find, in terms of 7, the x-coordinate of the point P. Show that the tangent PQ has equation 2x + 2y = ². Find the exact coordinates of Q. (iii) Show that the exact value of the area shaded in Fig. 8 isr(²-2).

1 Fig. 8 shows a sketch of part of the curve y=x sin 2x, where x is in radians. The curve crosses the x-axis at the point P. The tangent to the curve at P crosses the y-axis at Q. X P vy=x sin 2x Figh (i) Find Hence show that the x-coordinates of the turning points of the curve satisfy the equa dx tan 2x + 2x = 0. (ii) Find, in terms of 7, the x-coordinate of the point P. Show that the tangent PQ has equation 2x + 2y = ². Find the exact coordinates of Q. (iii) Show that the exact value of the area shaded in Fig. 8 isr(²-2).

Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter6: The Trigonometric Functions
Section: Chapter Questions
Problem 41RE
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1 Fig. 8 shows a sketch of part of the curve y = x sin 2x, where x is in radians. The curve crosses the x-axis at the point P. The tangent to the curve at P crosses the y-axis at Q. P y = x sin 2x Figh (i) Find Hence show that the x-coordinates of the turning points of the curve satisfy the equa dx tan 2x + 2x = 0). (ii) Find, in terms of 7, the x-coordinate of the point P. Show that the tangent PQ has equation 27x + 2y = ². Find the exact coordinates of Q. (iii) Show that the exact value of the area shaded in Fig. 8 is 7(x² − 2).
Transcribed Image Text:1 Fig. 8 shows a sketch of part of the curve y = x sin 2x, where x is in radians. The curve crosses the x-axis at the point P. The tangent to the curve at P crosses the y-axis at Q. P y = x sin 2x Figh (i) Find Hence show that the x-coordinates of the turning points of the curve satisfy the equa dx tan 2x + 2x = 0). (ii) Find, in terms of 7, the x-coordinate of the point P. Show that the tangent PQ has equation 27x + 2y = ². Find the exact coordinates of Q. (iii) Show that the exact value of the area shaded in Fig. 8 is 7(x² − 2).
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