Given the values for sin t and cos t, use reciprocal and quotient identities to find the values of the other trigonometric functions of t. sin t = 3/4 and cos t=sqrt7/4

Consider the given trigonometric function sint and cost.
The other trigonometric functions values are find as,
Use the trigonometric formula,
${\displaystyle \tan t=\frac{\sin t}{\cos t}}$
${\displaystyle \csc t=\frac{1}{\sin t}}$
${\displaystyle \sec t=\frac{1}{\cos t}}$
${\displaystyle \cot t=\frac{\cos t}{\sin t}}$
Now, substitute the given trigonometric function values in the above formula,
Since ${\displaystyle \sin t=\frac{3}{4}\text{and}\cos t=\frac{\sqrt{7}}{4}}$
Thus, ${\displaystyle \tan t=\frac{\sin t}{\cos t}=\frac{\frac{3}{4}}{\frac{\sqrt{7}}{4}}=\frac{3}{\sqrt{7}}}$
${\displaystyle \csc t=\frac{1}{\sin t}=\frac{1}{\frac{3}{4}}=\frac{4}{3}}$
${\displaystyle \sec t=\frac{1}{\cos t}=\frac{1}{\sqrt{\frac{3}{4}}}=\frac{4}{\sqrt{7}}}$
${\displaystyle \cot t=\frac{\cos t}{\sin t}=\frac{\frac{\sqrt{7}}{4}}{\frac{3}{4}}=\frac{\sqrt{7}}{3}}$