Answers:
1) [tex]cos B=\frac{4}{5}=0.8[/tex]
2) [tex]csc A=\frac{5}{3}=1.66[/tex]
3) [tex]sec B=\frac{5}{4}=1.25[/tex]
4) [tex]tan A=\frac{3}{4}=0.75[/tex]
5) [tex]z=38.65\°[/tex]
Step-by-step explanation:
First exercise:
We have a right triangle with the values of each side an we have to find the following trigonometic functions (taking into account the secant function [tex]sec[/tex] is the inverse of the cosine, the cosecant [tex]csc[/tex] is the inverse of the sine):
1) [tex]cos B=\frac{Adjacent-side}{hypotenuse}[/tex]
[tex]cos B=\frac{4}{5}=0.8[/tex]
2) [tex]csc A=\frac{1}{sin A}[/tex]
[tex]\frac{1}{sin A}=\frac{1}{\frac{5}{3}}[/tex]
Then:
[tex]csc A=\frac{5}{3}=1.66[/tex]
3) [tex]sec B=\frac{1}{cos B}[/tex]
[tex]frac{1}{cos B}=\frac{1}{\frac{4}{5}}[/tex]
Then:
[tex]sec B=\frac{5}{4}=1.25[/tex]
4) [tex]tan A=\frac{opposite-side}{adjacent-side}=\frac{3}{4}[/tex]
Then:
[tex]tan A=\frac{3}{4}=0.75[/tex]
Second exercise:
5) Here, we are given another right triangle and we have to find the measure of the angle [tex]z[/tex].
So, according to the figure, we can use the tangent function:
[tex]tan z=\frac{opposite-side}{adjacent-side}[/tex]
[tex]tan z=\frac{8}{10}[/tex]
Finding the value of [tex]z[/tex]:
[tex]z=tan^{-1}\frac{8}{10}[/tex]
[tex]z=38.65\°[/tex]
