We have to calculate the other trigonometric functions knowing that:
[tex]\begin{gathered} \sin t=\frac{1}{4} \\ \cos t=\frac{\sqrt[]{15}}{4} \end{gathered}[/tex]
We can calculate tan(t) as:
[tex]\tan t=\frac{\sin t}{\cos t}=\frac{\frac{1}{4}}{\frac{\sqrt[]{15}}{4}}=\frac{1}{\sqrt[]{15}}=\frac{\sqrt[]{15}}{15}[/tex]
We can calculate csc(t) as:
[tex]\csc t=\frac{1}{\sin t}=\frac{1}{\frac{1}{4}}=4[/tex]
We can calculate sec(t) as:
[tex]\sec t=\frac{1}{\cos t}=\frac{1}{\frac{\sqrt[]{15}}{4}}=\frac{4}{\sqrt[]{15}}=\frac{4\sqrt[]{15}}{15}[/tex]
We can calculate cot(t) as:
[tex]\cot t=\frac{1}{\tan t}=\frac{1}{\frac{1}{\sqrt[]{15}}}=\sqrt[]{15}[/tex]
Answer:
tan(t) = (√15)/15
csc(t) = 4
sec(t) = 4(√15)/15
cot(t) = √15
