Trigonometric Identity for Tangent
The tangent of an angle ($A$) in trigonometry is defined as the ratio of the sine of the angle to the cosine of the angle. This fundamental relationship is expressed as:
$ \tan A = \frac{\sin A}{\cos A} $
Calculating tan A
We are given the following values:
- $\sin A = 0.6$
- $\cos A = 0.8$
Substitute these values directly into the trigonometric identity:
$ \tan A = \frac{0.6}{0.8} $
To simplify the calculation, we can remove the decimal points by multiplying the numerator and denominator by 10:
$ \tan A = \frac{6}{8} $
Now, simplify the fraction by dividing both the numerator and the denominator by their greatest common divisor, which is 2:
$ \tan A = \frac{6 \div 2}{8 \div 2} = \frac{3}{4} $
Finally, convert the fraction to its decimal form:
$ \tan A = 0.75 $
Result
The value of $\tan A$ is 0.75.
Similar Questions
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