Download OE OF OG 4 cm = = = , EOG 90 and FOG x ∠ = ° ∠ = °. A 8sinx

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
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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
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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
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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 
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