Draw ∆ABC, in which LB=90°.write Sin A, Cos A and tan A in terms of it's sides
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Answer:
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Here ∠CAB is an acute angle. Observe the position of the sides with respect to angle A.
- BC is the opposite side of Angle A.
- AB is the adjacent side with respect to angle A.
- AC is the hypotenuse of the right angled triangle ABC.
The trigonometric ratios of the angle A in the right angled triangle ABC can be defined as follows.
sinA=
Hypotenuse
SideoppositetoangleA
=
AC
BC
cosA=
Hypotenuse
SideadjacenttoangleA
=
AC
AB
tanA=
SideadjacenttoangleA
SideoppositetoangleA
=
AB
BC
cscA=
SideoppositetoangleA
Hypotenuse
=
BC
AC
secA=
SideadjacenttoangleA
Hypotenuse
=
AB
AC
cotA=
SideoppositetoangleA
SideadjacenttoangleA
=
BC
AB
Now let us define the trigonometric ratios for the acute angle C in the right angled triangle, ∠ABC=90
o
Observe that the position of the sides changes when we consider angle 'C' in place of angle A.
sinC=
AC
AB
cosC=
AC
BC
tanC=
BC
AB
cscC=
AB
AC
secC=
BC
AC
cotC=
AB
BC
solution
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