Question

given the following trig equations find the exact value of the remaining five trig functions.cos0 = 4/9 where sin0 < 0( sin, tan, csc, cot, sec)

Answer 1

we have that:

`\sin ^2\theta=1-\cos ^2\theta=1-(16)/(81)=(65)/(81)\rightarrow\sin \theta=-\frac{\sqrt[]{65}}{9}`

having this we get that

`\tan \theta=\frac{-\sqrt[]{65}}{4},\cot \theta=-\frac{4}{\sqrt[]{65}},\sec \theta=(9)/(4),\csc \theta=-\frac{9}{\sqrt[]{65}}`