Calculus I - Week 02 Notes

Paper Exercises

Exercise 02-01

01

Forms of a parabola

The graph of the function $f(x)=2x^2-12x+2$ is a parabola. Put this parabola in vertex form. What is the vertex point?

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Exercise 02-02

02

Trig identities

• (a) Write a formula for $\cos \theta$ in terms of $\sin \theta$. (Hint: use a trig identity, or draw a triangle.)
• (b) Show how to derive the identity $$1+{\cot }^2\theta ={\csc }^2\theta$$ from the “most important” trig identity.

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Exercise 02-03

03

Hyperbolic sum rule

Verify the “hyperbolic sum rule:” $$\sinh (x+y)=\sinh (x)\cosh (y)+\cosh (x)\sinh (y)$$

(You should plug in the definitions in terms of exponentials, expand the RHS, and simplify.)

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