Question

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

Analytic geometry
ANSWERED
asked 2020-11-08
Find the six function values of \(\displaystyle{8}^{\circ}\) in terms of p, q and r, if
\(\displaystyle{{\sin{{82}}}^{\circ}=}{p}\)
\(\displaystyle{{\cos{{82}}}^{\circ}=}{q}\)
\(\displaystyle{{\tan{{82}}}^{\circ}=}{r}\)

Answers (1)

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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