Answer
$sin\theta=-\frac{7}{25}$;
$tan\theta=-\frac{7}{24}$;
$cot\theta=-\frac{24}{7}$;
$sec\theta=\frac{25}{24}$;
$csc\theta=-\frac{25}{7}$
Work Step by Step
1. Given $cos\theta=\frac{24}{25}$ with $\theta$ in quadrant IV, form a right triangle of sides $7,24,25$ with angle $\theta$ facing side $7$, we have:
2. $sin\theta=-\frac{7}{25}$
3. $tan\theta=-\frac{7}{24}$
4. $cot\theta=-\frac{24}{7}$
5. $sec\theta=\frac{25}{24}$
6. $csc\theta=-\frac{25}{7}$
