Need help with the integration of attached problem

[Shahryar]

Kindly can someone tell me how can i integrate and plot the following formula as a function of time. while theta is changing from 1 to 20.
also attached .docx file for convenience. Any kind of help or advice will be highly appreciable.

 

[berkeman]

Where is the problem from? Is it for schoolwork?

 

[Shahryar]

Where is the problem from? Is it for schoolwork?

No its in my engineering design problem. I am just stuck here. I need to plot the graph for theta as a function of time. I am not really good in calculus to be honest.
May be i can use MATLAB to solve !

 

[berkeman]

No its in my engineering design problem.

What does that mean? An engineering design project for what year in university? An engineering project for work? Where do you work?

 

[HallsofIvy]

It would strike me as an obvious first step to use the facts that $sin(20- \theta)= sin(20)cos(\theta)- cos(20)sin(\theta)$ and $cos(20- \theta)= cos(20)cos(\theta)+ sin(20)sin(\theta)$.

That "20" looks strange for radian measure. If it is in degrees you should remember that $\int sin(x)dx= -cos(x)+ C$ and $\int cos(x)= sin(x)+ C$ only for x measured in radians.

 

[Shahryar]

It would strike me as an obvious first step to use the facts that $sin(20- \theta)= sin(20)cos(\theta)- cos(20)sin(\theta)$ and $cos(20- \theta)= cos(20)cos(\theta)+ sin(20)sin(\theta)$.

That "20" looks strange for radian measure. If it is in degrees you should remember that $\int sin(x)dx= -cos(x)+ C$ and $\int cos(x)= sin(x)+ C$ only for x measured in radians.

Yes that 20 is actually 20 degrees. should i convert it into radians which is 0.34906585 radians ?