# Introduction to Calculus/Quiz 1

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