Question

5sinx+12cosx=7 then5 cosx-12sinx=?​

Answer 1

Step-by-step explanation:

The maximum value for 5 \sin x+12 \cos x + 135sinx+12cosx+13 is 18 and the minimum value for 5 \sin x+12 \cos x + 135sinx+12cosx+13 is 25

To find:

The maximum and minimum values of 5 \sin x+12 \cos x + 135sinx+12cosx+13

Solution:

Given that

5 \sin x+12 \cos x + 135sinx+12cosx+13

The minimum value means zero and the maximum value means 90.

If the function,y=f(x)y=f(x) , by using differentiation we will find the maximum and minimum value.

Maximum and minimum occur when \mathrm { f } ^ { \prime } ( \mathrm { x } ) = 0 \text { i.e. } \frac { \mathrm { dy } } { \mathrm { dx } } = 0f

′

(x)=0 i.e.

dx

dy

=0

x = a is a maximum

\text { if } \mathrm { f } ^ { \prime } ( \mathrm { a } ) = 0 \text { and } \mathrm { f } ^ { \prime \prime } ( \mathrm { a } ) < 0 if f

′

(a)=0 and f

′′

(a)<0

x=a is a minimum

\text { if } f ^ { \prime } ( a ) = 0 \text { and } f ^ { \prime \prime } ( a ) > 0 if f

′

(a)=0 and f

′′

(a)>0

Maximum value of x=90

\begin{lgathered}\begin{array} { l } { = 5 \sin 90 + 12 \cos 90 + 13 } \\\\ { = 5 \times 1 + 12 \times 0 + 13 } \\\\ { = 5 + 13 } \\\\ { = 18 } \\\\ { 5 \sin x + 12 \cos x + 13 = 18 } \end{array}\end{lgathered}

=5sin90+12cos90+13

=5×1+12×0+13

=5+13

=18

5sinx+12cosx+13=18

Minimum value of the x=0

\begin{lgathered}\begin{array} { l } { = 5 \times \sin 0 + 12 \times \cos 0 + 13 } \\\\ { = 5 \times 0 + 12 \times 1 + 13 } \\\\ { = 0 + 12 + 13 } \\\\ { = 25 } \end{array}\end{lgathered}

=5×sin0+12×cos0+13

=5×0+12×1+13

=0+12+13

=25

Result:

The maximum value for 5 \sin x+12 \cos x + 135sinx+12cosx+13 is 18 and the minimum value for 5 \sin x+12 \cos x + 135sinx+12cosx+13 is 25

Answer 2

Answer:

Step-by-step explanation:

5sinx+12cosx=13

differentiate with respect to x

5(cosx)+12(-sinx)=0

5cosx-12sinx=0