Question

the angle t is an acute angle and sin t and cost t are given. Use identities to find tan t , csc t, sec t, and cot t. where necessary, rationalize demonstrations.sin t= 7/25, cos t= 24/25

Answer 1

Answer:

tan t = 7/24

csc t = 25/7

sec t = 25/24

cot t = 24/7

Explanation:

From the question, we're told that sin t = 7/25 and cos t = 24/25. Since we know the identities of sine and cosine to be as follows we can go ahead and determine tan t as shown below;

$\begin{gathered} \sin t=\frac{opposite}{\text{hypotenuse}}=\frac{7}{25} \\ \cos t=\frac{adjacent}{\text{hypotenuse}}=\frac{24}{25} \\ \therefore\tan t=\frac{opposite}{\text{adjacent}}=\frac{7}{24} \end{gathered}$

Let's go ahead and find cosecant t (csc t);

$\csc t=\frac{1}{\sin t}=\frac{1}{\frac{7}{25}}=1\times\frac{25}{7}=\frac{25}{7}$

For sec t, we'll have;

$\sec t=\frac{1}{\cos t}=\frac{1}{\frac{24}{25}}=1\times\frac{25}{24}=\frac{25}{24}$

For cot t;

$\cot t=\frac{1}{\tan t}=\frac{1}{\frac{7}{24}}=1\times\frac{24}{7}=\frac{24}{7}$