Trigonometrical Formulae
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Transcript of Trigonometrical Formulae
7/18/2019 Trigonometrical Formulae
http://slidepdf.com/reader/full/trigonometrical-formulae 1/1
Hyp.
r
·
(iii) sec x = = -
Base
p
Base b
iv)
cos y = =-
Hyp.
n
t
Base b
v)
.co y = -
Perp. m
Hyp. n
vi) cosec y = -
Perp.
m
vii)
. Perp.
u
Stn Z =
= -
Hyp. n
Base
k
viii)
cos
z
=
= -
Hyp. n
Perp. u
tan z = =-
A
s
Base k
0
•
xi)
Q. 2.
In the given figure, LB
90°,
AB
= 4
units and BC = 3 units. Find :
A
i) sin A (ii) cos A
i i i) cot A
v) sec C
iv)
sin C
vi) tan C
4 units
c
B
Sol.
In
MBC,
LB
=
90°
AB
=
4
units and BC =
3
units
But AC
2
=
AB
2
+ BC2
•
. .
Now
Pythagoras Theorem)
=
4)2 + 3)2
= 16
+9
=
25
= 5)
2
AC= 5 units
i) sin A
=
Perp.
=
BC
= .
Hyp. AC 5
(ii) cos A = Base = AB = i
Hyp. AC 5
cot A = Base = AB = i
Perp. BC
3
iii)
sin C = Perp.
=
AB
=
i
Hyp. AC 5
iv)
v)
sec C =
Hyp.
= AC =
Base BC 3
Perp. AB 4
vi) tan C = = = - Ans
Base BC 3 ·
Q. 3.
From the given figure, write down the
values
of:
i)
sin B (ii) tan B
(iii) cos c
iv)
cot c
v)
sin B cos C
+cos
B sin
C)
vi) sec
2
C - tan
2
C)
A
L ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ c
17 units
Sol. In MBC,
LA
90°
BC = 17 units, AB = 15 units
But BC
2
= AB
2
+
AC2
Pythagoras Theorem)
>
17)
2
=
15)
2
+ AC
2
>
289 = 225
AC
2
> AC
2
= 289
- 225
=
64
=
8)
2
,
:. AC= 8
units
r·)
sin B = Perp. =AC =
_. _
1
Hyp. BC 17
ii) tan B = Perp. = AC =
_ _
Base AB
15
(iii) cos
C
=
Base =
AC
= _ _
Hyp.
BC
17