The purpose of calculating tangents without a calculator is to develop a deeper understanding of the concept of tangents and their relationship to other trigonometric functions. It also helps to improve one's mental math skills.
To calculate a tangent without a calculator, you can use the tangent ratio formula which is tan(theta) = opposite/adjacent. You can also use the unit circle and SOH-CAH-TOA method to find the tangent value.
While it is not necessary to calculate tangents without a calculator in everyday life, it is a fundamental skill for students studying trigonometry and can also be useful in certain professions such as engineering and navigation.
Sure, let's say we want to find the tangent of 45 degrees. Using the tangent ratio formula, we have tan(45) = opposite/adjacent. Since we know that in a 45-45-90 degree triangle, the opposite and adjacent sides are equal, we can say that tan(45) = 1/1 = 1. So the tangent of 45 degrees is 1.
You can use a calculator to check if your calculated tangent value is accurate. Simply enter the angle in degrees and take the tangent of it. If the value matches your calculated value, then it is accurate. You can also use trigonometric identities and special angles to verify your answer.