Introduction to Calculus/Quiz 1

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1. Express $\tan (\theta )$ in terms of $\sin (\theta )$
2. If $\csc (\theta )=1/x,$ then what does $x$ equal?
3. Prove ${\tan }^2(\theta )+1={\sec }^2(\theta )$ using ${\sin }^2(\theta )+{\cos }^2(\theta )=1$
4. $\cos (A+B)=\cos (A)\cos (B)-\sin (A)\sin (B)$
   • Find the double angle idenities for the cosine function using the above rule.
   • Find the half angle idenities from the double angle idenities.
   • Find the value of ${\cos }^2(\theta )$ without exponents using the above rules.
   • (Challenge) Find the value of ${\cos }^3(\theta )$ without exponents.