Answer
1. $cos\theta =\frac{3}{5}$,
2. $tan\theta =\frac{4}{3}$,
3. $cot\theta =\frac{3}{4}$,
4. $sec\theta =\frac{5}{3}$,
5. $csc\theta =\frac{5}{4}$.
Work Step by Step
Given $sin\theta=\frac{4}{5}$ with $\theta$ in quadrant I, let $y=4, r=5$, we have $x=\sqrt {5^2-4^2}=3$, thus:
1. $cos\theta=\frac{x}{r}=\frac{3}{5}$,
2. $tan\theta=\frac{y}{x}=\frac{4}{3}$,
3. $cot\theta=\frac{1}{tan\theta}=\frac{3}{4}$,
4. $sec\theta=\frac{1}{cos\theta}=\frac{5}{3}$,
5. $csc\theta=\frac{1}{sin\theta}=\frac{5}{4}$.
