Survey
* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
TOPIC 34 | differentiation of trigonometric functions set 1 of 7 get the full set details at the bottom of page Question 1: The diagram shows two isosceles triangles EOF and FOG where OE = OF = OG = 4 cm , ∠EOG =° 90 and ∠FOG = x° . The area of the quadrilateral OEFG is A cm2. E F 4 cm O G 4 cm (i) Show that = A 8 sin x + 8cos x . (ii) Express A in the form R sin( x + α ) . (iii) Find the maximum value of A and the corresponding value of x. (iv) Given that x can vary, find the values of x when A = 10. Question 2: Differentiate cos 3 (6x − 3) with respect to x. Question 3: Given that y = x 2 sin 3x , find the value of dy when x = 2 . dx Question 4: Differentiate e 2x tan x with respect to x. Question 5: P 1m Q W V 2m R S T U Page Confused? Want to improve in this topic? This topic’s home tuition is available Lessons Required: 01 (2 hours, $40/hour) BOOK now to get FULL PRACTICE SET free M: 8429 5372 E: [email protected] |1 TOPIC 34 | differentiation of trigonometric functions set 1 of 7 get the full set details at the bottom of page The diagram shows a vertical section through a tent in which PQ = 1 m , ∠QRS = QR = 2 m and ∠QPT = θ (in radians). The diagram is symmetrical about the vertical PT and both QV and RT are horizontal. (i) Show that = PT cosθ + 2sinθ . (ii) Given that θ varies, find the maximum length of PT and the corresponding value of θ Question 6: Differentiate tan 2 ( 3x + 1) with respect to x. Question 7: Differentiate cos(1 − 2x 3 ) with respect to x. Question 8: e 2x with respect to x. Differentiate and simplify sin x Question 9: Given that y = e 2x cos 3x , find the value of dy when x = 1. dx Question 10: Differentiate sin2 2x − cos x with respect to x. Question 11: Differentiate x tan 2 x with respect to x. Question 12: Differentiate the following with respect to x: cos 3 x Question 13: 9x 3x 2 . Given that y = cos sin 3x , show that y ′ = 2 2 sin 3x 3cos Page Confused? Want to improve in this topic? This topic’s home tuition is available Lessons Required: 01 (2 hours, $40/hour) BOOK now to get FULL PRACTICE SET free M: 8429 5372 E: [email protected] |2 TOPIC 34 | differentiation of trigonometric functions set 1 of 7 get the full set details at the bottom of page Question 14: C D B A X In the figure, ABCD is a square of side of 20 cm and ∠BAX = θ radians, y is the distance from C to the horizontal line AX. (i) Express y in terms of θ . (ii) Find an expression for the approximate change in y as θ increases from π 6 by a small amount p. [Leave your answer in surd form] Question 15: Differentiate 3sin 3 ( 2x + 1) with respect to x, simplifying your answers as far as possible. Question 16: Differentiate ( x 3 − 1)cos 3x with respect to x. Question 17: = y sin 4x + cos 4 x , find the value of Given that dy π when x = . 4 dx Question 18: Differentiate with respect to x tan 3 2x Question 19: A curve has the equation y = sin x . 2 − cos x dy 2cos x − 1 . = 2 dx ( 2 − cos x) (ii) the values of x between 0 and 2π for which y is stationary. (i) Show that Page Confused? Want to improve in this topic? This topic’s home tuition is available Lessons Required: 01 (2 hours, $40/hour) BOOK now to get FULL PRACTICE SET free M: 8429 5372 E: [email protected] |3 TOPIC 34 | differentiation of trigonometric functions set 1 of 7 get the full set details at the bottom of page Question 20: 1 − cot 2 x Prove the identity ≡ sin 2 x − cos 2 x . 2 1 + cot x d 1 − cot 2 x Hence, or otherwise, find . dx 1 + cot 2 x Page Confused? Want to improve in this topic? This topic’s home tuition is available Lessons Required: 01 (2 hours, $40/hour) BOOK now to get FULL PRACTICE SET free M: 8429 5372 E: [email protected] |4