2023-2024

THE SEZIN SCHOOL

MATHEMATICS DEPARTMENT
SEMESTRE HOMEWORK-1

NAME SURNAME : ………………………………………………………… Grade : 11

NUMBER :……….

2p 5p
1) Find the principal angle of the following: [ 3200 ,3000 , 2100 , , ]
3 4
50p 27p
a) 32000 b) -600 c) 9300 d) e) -
3 4

2) Find the value of the following:

æ 3p ö æp ö p p
a) sin ç - ( )
÷ + cos -p + tan -2p [0] ( ) b) tan2 ç ÷ + cot - 2sin + sin p [3]
è 2 ø è3ø 6 3

p p p æ pö æ pö æ pö
c) sin2 - 2cos2 - 5tan2 [-5] d) cos3 ç - ÷ - cot3 ç - ÷ + sin3 ç - ÷ [3 3 ]
4 3 4 è 3ø è 6ø è 6ø

tanx - sinx secx

3) Simplify - = ? [0]
sin x
3
1 + cosx

sin3 x + cos3 x 1 - sin x.cos x

4) Prove that ÷ =1
sin2 x - cos2 x sin x - cos x

2 sin3 x + cos3 x é 7 ù
5) If tan x = then find the value of ê ú
3 sin x + cos x ë 13 û
 1 1
6) + .sin20 = ? [ 2 ]
1 + cos200 1 - cos200

1 1
7) If + =4 and 0o < x < 90o find the value of x. [450]
1 - sin x 1 + sin x

sin2 155 + cos2 385 a

8) tan25 = a find interms of a. [ ]
tan205 + cot335 2
a -1

Π
cos( - a).tanx 3
Π 2
9) If 27 Cosx = 81Sinx and a +b = then find . [ ]
2 Π 5
sin( - b).secx
2

2a - 1 b +1
10) a, b Î R and sinx= and cosx= , find the interval for a+b. [ -6 £ a + b £ 5 ]
3 4

2 -13 17
11) If 2m - 3sin2x + = 0 then find the value of m [ £m£ ]
5 10 10
 æ Ù ö
12) There is a unit circle, m ç POA ÷ = a then find area of shaded
ç ÷
è ø
cos3 a
region. [ ]
2sin a

1 æ Ù ö 3
13) There is a unit semicircle, [AK] ⊥ [OA], |PK| = u, m ç POA ÷ = a then find tanα. [ ]
4 ç ÷ 4
è ø

14) If there are six equal squares in the figure then find tanx . [3]

15) Arrange the trigonometric ratiof of a = cos285° , b = tan233°, c = sin127° , d = cot21°. [ d > b > c > a ]

16) Which of the following is true: [I-IV]

p
I. 0 < x < y < ⇒ sinx < siny
2
p
II. 0 < x < y < ⇒ cosx < cosy
2
p
III. < x < y < π ⇒ sinx < siny
2
3p
IV. π < x < y < ⇒ tanx < tany
2

17) Which of the following is true: [II]

I. sin130° > sin132°
II. cos130° > cos132°
III. tan134° > sin271°
IV. sin165° > tan195°
 æ 5p ö
cos ç -
2
(
+ x ÷ .cot 5p - x )
18) Simplify è ø [-1]
æ 3p ö æ 17p ö
sin ç + x ÷ tan ç - ÷
è 2 ø è 4 ø

sin(x - 90° ) + sin(270° - x)

19) Simplify . [1]
cos(180° - x) - cos( -x)

æ 35p ö
( )
cos x - 13p - sin ç (
+ x ÷ - tan x - 50p )
è 2
20) Simplify
æ 23p ö
ø
æ 41p ö
[1]
cos ç (
- x ÷ + sin 31p - x + cot ç) +x÷
è 2 ø è 2 ø

æ 3 1 3ö æ 1ö 3
21) tan ç 5 arctan - arcsin ÷ [-1] 22) sin ç 3arctan 3 + 2arccos ÷ [- ]
ç
è 3 4 2 ÷ø è 2ø 2

1
(
23) If cos arctan x = ) then find x. [ x ÎR ]
1+ x2

æ æ 3 öö æ æ 12 ö ö -14
24) Find the result of sin ç tan -1 ç - ÷ ÷ + cos ç arcsin ç ÷ ÷ . [ ]
ç ÷ ç ÷
è è 4 øø è è 13 ø ø 65
 æ æ æ 12 ö ö ö é 5 ù
25) Find the result of tan ç sin -1 ç sin ç arccos ÷ ÷ ÷ . ê ú
ç ç 13 ø ÷ø ÷ø ë 12 û
è è è

26) In triangle ABC, |BD|=4 u, |BE|=5 u, |EC|=3 u, |AD|=6 u, |DE|=6 u, |AC|=x then find the value of x. [12]

æÙö
27) If ABCD is a rhombus, |AB|=3 u, |BE|=|DF|=1 u, m ç A ÷ = 120 then find the value of |EF|. [ 13 ]
o

è ø

æ Ù ö æ Ù ö
28) In ABC triagle, m ç BAC ÷ = 45 , m ç ABC ÷ = 60 , BC = 3 2 u then find |AC|.
o o

è ø è ø
é3 3 ù
ëê úû

29) In ABC triagle,

|AE| = 6 u
|EC| = 3 u
|DC| = 4 u
|BD| = x u
If area of shaded regions are equal then find x. [8]
30) In ABC triangle
|AB| = 10 u, |BC| = 12 u, |AD| = 2|DC|
æ Ù ö æ Ù ö 5 3
m ç DBC ÷ = a , m ç ABD ÷ = 60o , find sina. [ ]
è ø è ø 24

31) In ABC right triangle

|AD| = 8 u, |AB| = 5 u, |BC|=12 u
[AD] ^ [AC], [AB] ^ [BC]
æ D ö 100
find A ç ABD ÷ [ ]
è ø 13

32) If B(0,-1) and D(0,4) are given then find the area of ABCD
25 y
quadrilateral. [ ]
4
D(0,4)

A
. O C x

.
B(0,-1)

33) ABCD is arectangle, find the coordinates of point D. [(8,-3)]

34) Find the coordinates of point B such that éëAB ùû Ç éëEC ùû = {D} , A(-3, 14),
E(-1, 6), C(7,4) |ED|=|DC| and 2|AD|=3|BD|. [B(7,-1)]

AC 2
35) For C Î éëAB ùû , A(-1, 4) and B(4, -6) are given. If = then find product of coordinates of C. [0]
BC 3

36) If the lines (m + 1)x + y – 2 = 0 and 3x + (m - 1)y + 1 = 0 are parallel to each other then find the product of
m values. [-4]

37) ABCD is a triangle as shown in the figure. If D(3,5) and |AK|=2|KD| are
given then find the equation of line d. [2y-3x-4=0]

38) B is a vertex of OABC rectangle, on line d. If |AB|=2|OA|, D(2,0) and

72
E(0,3) then find the area of the rectangle. [ ]
49

39) According to given figure, the lines d1 and d2 are perpendicular to each
other on y-axis. Find the equation of line d2. [3y+x-9=0]
40) ABC is an equilateral triangle where B(2, -4) is given. If [AC]is on the line 6x - 8y + 16 = 0 then find the
length of height B. [6]

41) If B( - 1 ; 6 ) C( -4 ; 0) then find the coordinates of E. [(11,0)]

y

A [ AC ] ^ [EB ]
B D

C E x

42) If the distance from the point A(–1,2) to the line 5x + 12y = –k is 2 u, find the value(s) of k. [7,-45]

16
43) Find the value of k if the distance between the lines 5x – 12y – 8 = 0 and 10x – 24y + k = 0 is 2k units. [ ]
51

44) Sketch the region in the -plane defined by the equation or inequalities.
x
a) -1 £ y £ 3 b) y < 2 , x < 4 c) y < 1 -
2