bitterstkk6

2023-03-03

Given that t is in quadrant II and sin(t)=(7/25), find the exact values of cos(t), tan(t), cot(t), sec(t), and csc(t).

Prince Neal

Beginner2023-03-04Added 5 answers

$\mathrm{sin}t=\frac{7}{25}$, this mean $\mathrm{cos}}^{2}t=1-{\mathrm{sin}}^{2}t=1-\frac{49}{625}=\frac{576}{25$

It in Quadrant II, so cos t - negative, and $\mathrm{cos}t=-\frac{24}{25}$

$\mathrm{tan}t=\frac{\mathrm{sin}}{\mathrm{cos}}=\left(\frac{7}{25}\right)(-\frac{25}{24})=-\frac{7}{24}$

$\mathrm{cot}t=\frac{1}{\mathrm{tan}}=-\frac{24}{7}$

$\mathrm{sec}t=\frac{1}{\mathrm{cos}}=-\frac{25}{24}$

$\mathrm{csc}t=\frac{1}{\mathrm{sin}}=\frac{25}{7}$

It in Quadrant II, so cos t - negative, and $\mathrm{cos}t=-\frac{24}{25}$

$\mathrm{tan}t=\frac{\mathrm{sin}}{\mathrm{cos}}=\left(\frac{7}{25}\right)(-\frac{25}{24})=-\frac{7}{24}$

$\mathrm{cot}t=\frac{1}{\mathrm{tan}}=-\frac{24}{7}$

$\mathrm{sec}t=\frac{1}{\mathrm{cos}}=-\frac{25}{24}$

$\mathrm{csc}t=\frac{1}{\mathrm{sin}}=\frac{25}{7}$