# Find the six function values of 8^circ in terms of p, q and r, if sin82^circ=p cos82^circ=q tan82^circ=r

Question
Analytic geometry
Find the six function values of $$\displaystyle{8}^{\circ}$$ in terms of p, q and r, if
$$\displaystyle{{\sin{{82}}}^{\circ}=}{p}$$
$$\displaystyle{{\cos{{82}}}^{\circ}=}{q}$$
$$\displaystyle{{\tan{{82}}}^{\circ}=}{r}$$

2020-11-09
Recall that,
$$\displaystyle{c}{s}\otimes={\sin{{\left({90}^{\circ}-{x}\right)}}},$$
$$\displaystyle{\sin{{x}}}={\cos{{\left({90}^{\circ}-{x}\right)}}},$$
$$\displaystyle{\cot{{x}}}={\tan{{\left({90}^{\circ}-{x}\right)}}},$$
$$\displaystyle{\tan{{x}}}={\cot{{\left({90}^{\circ}-{x}\right)}}},$$
Therefore,
$$\displaystyle{{\sin{{8}}}^{\circ}=}{{\cos{{82}}}^{\circ}}$$
$$\displaystyle{{\sin{{8}}}^{\circ}=}{q}$$
$$\displaystyle{{\cos{{8}}}^{\circ}=}{{\sin{{82}}}^{\circ}}$$
$$\displaystyle{{\cos{{8}}}^{\circ}=}{p}$$
$$\displaystyle{{\cot{{8}}}^{\circ}=}{{\tan{{82}}}^{\circ}}$$
$$\displaystyle{c}{\quad\text{or}\quad}{8}^{\circ}={r}$$
$$\displaystyle{{\csc{{8}}}^{\circ}=}\frac{{1}}{{{\sin{{8}}}^{\circ}}}$$
$$\displaystyle{{\csc{{8}}}^{\circ}=}\frac{{1}}{{q}}$$
$$\displaystyle{{\sec{{8}}}^{\circ}=}\frac{{1}}{{{\cos{{8}}}^{\circ}}}$$
$$\displaystyle{{\sec{{8}}}^{\circ}=}\frac{{1}}{{p}}$$
$$\displaystyle{{\tan{{8}}}^{\circ}=}\frac{{1}}{{{\cot{{8}}}^{\circ}}}$$
$$\displaystyle{{\tan{{8}}}^{\circ}=}\frac{{1}}{{r}}$$

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