Question

Suppose cos(a)=.325

Answer 1

The value of tan a is 2.9098

Explanation:

The given value is $\cos (a)=0.325$

Now, we shall find the value of sin (a), using the identity,

$\sin ^2(a)+\cos^2(a)=1$

Substituting the value of cos (a), we get,

$\sin ^2(a)+(0.325)^2=1\\\sin ^2(a)+0.1056=1$

Subtracting both sides by 0.1056, we have,

$\sin ^2(a)=0.8944$

Taking square root on both sides, we get,

$sin a= 0.9457$

Now, we shall substitute the value of sin (a) and cos (a) to determine the value of tan (a) in the identity $tan (a) =\frac{sin(a)}{cos(a)}$

$tan (a) =\frac{0.9457}{0.325}\\tan (a) = 2.9098$

Thus, the value of tan (a) is 2.9098