Question

watch the video and then solve the problem given below. click here to watch the video. the angle t is an acute angle and sin t and cos t are given. use identities to find tan t, csc t, sec t, and cot t. where necessary, rationalize denominators. sin t = \frac{1}{5}, cos t = \frac{2\sqrt{6}}{5}

Explanation:

Step1: Recall tangent formula

$\tan t=\frac{\sin t}{\cos t}$
Substitute $\sin t = \frac{1}{5}$ and $\cos t=\frac{2\sqrt{6}}{5}$:
$\tan t=\frac{\frac{1}{5}}{\frac{2\sqrt{6}}{5}}=\frac{1}{2\sqrt{6}}=\frac{\sqrt{6}}{12}$

Step2: Recall cosecant formula

$\csc t=\frac{1}{\sin t}$
Substitute $\sin t=\frac{1}{5}$:
$\csc t = 5$

Step3: Recall secant formula

$\sec t=\frac{1}{\cos t}$
Substitute $\cos t=\frac{2\sqrt{6}}{5}$:
$\sec t=\frac{5}{2\sqrt{6}}=\frac{5\sqrt{6}}{12}$

Step4: Recall cotangent formula

$\cot t=\frac{\cos t}{\sin t}$
Substitute $\sin t=\frac{1}{5}$ and $\cos t=\frac{2\sqrt{6}}{5}$:
$\cot t = 2\sqrt{6}$

Answer:

$\tan t=\frac{\sqrt{6}}{12},\csc t = 5,\sec t=\frac{5\sqrt{6}}{12},\cot t = 2\sqrt{6}$