Respuesta :
The value of tan a is 2.9098
Explanation:
The given value is [tex]\cos (a)=0.325[/tex]
Now, we shall find the value of sin (a), using the identity,
[tex]\sin ^2(a)+\cos^2(a)=1[/tex]
Substituting the value of cos (a), we get,
[tex]\sin ^2(a)+(0.325)^2=1\\\sin ^2(a)+0.1056=1[/tex]
Subtracting both sides by 0.1056, we have,
[tex]\sin ^2(a)=0.8944[/tex]
Taking square root on both sides, we get,
[tex]sin a= 0.9457[/tex]
Now, we shall substitute the value of sin (a) and cos (a) to determine the value of tan (a) in the identity [tex]tan (a) =\frac{sin(a)}{cos(a)}[/tex]
[tex]tan (a) =\frac{0.9457}{0.325}\\tan (a) = 2.9098[/tex]
Thus, the value of tan (a) is 2.9098
