AP EAMCET Engineering 2018 Apr 22 Shift 1 Paper

Let y=cos(x),x=30° and x+Δx=31°
The value of
(y)x→

π

6

=cos(

π

6

)=

√3

2

Then, Δx=1°=0.0174 radian
Consider the given function
y=f(x)=cos(x)
Differentiate the above expression with respect to x

dy

dx

=−sin(x)
(

dy

dx

)x→

x

6

=−sin(

π

6

)
(

dy

dx

)x→

x

6

=−

1

2

Let Δy be the change in y due to the change Δr in x
Δy=

dy

dx

×Δx
=(−

1

2

)×0.0174
=(−0.5)×0.0174≈−0.0087
f(36°)=y+Δy
After solving this
=

√3

2

−0.0087
=

1.732

2

−0.0087
=0.8660−0.0087
=0.8573