Riemann Sums example Ch8 Q1iii

 

Understanding Polar Coordinates

 

Express $\cos^5t$ in terms of $\cos 5t,\cos3t,\cos t$ and express $\sin^4t$ in terms of $\cos 4t, \cos 2t$

• Other examples like this one are contained in the Algebra Notes Ch3 page 98 Example 3 and 4 ! Please also read this book, as it has many useful examples!!
• RTB - Read the Book 😎

Basic Riemann Sum for $I=\displaystyle\int^5_0x(5-x)\,dx$ with 5 intervals.

  

Riemann Sums (Upper and Lower) for an increasing function $y=f(x)$ on partition $\mathcal{P}=\left\{0,\dfrac{1}{n},\dfrac{2}{n},\cdots, \dfrac{n-1}{n},1\right\}$

  

Polar graph $r=2+\sin\theta$.

  

Polar graph $r=3+\cos\theta$.

  

Polar Graph blank 1

  

Sketch the ray $\text{Arg}\ (z-(3+2i))=\dfrac{\pi}{4}$

  

Find the square roots of $i$ in two ways, Cartesian and Mod-Arg way.