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.