Calculating Trigonometric Values: Solving Problems with Given Information

Introduction: Understanding Trigonometric Values

Trigonometric functions play a crucial role in various fields such as engineering, physics, mathematics, and science. Trigonometric values are used for solving problems related to angles, distances and heights in these fields. Understanding how to calculate trigonometric values is, therefore, an essential skill for anyone working in these fields.

In this blog, we will discuss how to calculate trigonometric values, including sine, cosine, and tangent. We will also explore how to use this knowledge to solve problems with the given information.

Body: Calculating Trigonometric Values

Sine:

Sine function is used to calculate the ratio of the opposite side of an angle to the hypotenuse. The formula for sine is:

sin (θ) = Opposite Side / Hypotenuse

For example, if we are given an angle of 35 degrees and the length of the opposite side as 8 cm, and the hypotenuse as 10cm, we can calculate the sine value as follows:

sin (35) = 8/10 = 0.8

Cosine:

Cosine function is used to calculate the ratio of the adjacent side of an angle to the hypotenuse. The formula for cosine is:

cos (θ) = Adjacent Side / Hypotenuse

For example, if we are given an angle of 55 degrees and the length of the adjacent side as 6 cm, and the hypotenuse as 10cm, we can calculate the cosine value as follows:

cos (55) = 6/10 = 0.6

Tangent:

Tangent function is used to calculate the ratio of the opposite side of an angle to the adjacent side. The formula for tangent is:

tan (θ) = Opposite Side / Adjacent Side

For example, if we are given an angle of 40 degrees and the length of the opposite side as 7 cm, and the adjacent side as 9 cm, we can calculate the tangent value as follows:

tan (40) = 7/9 = 0.78

Solving Problems with Given Information

Trigonometric values are commonly used to solve problems related to angles, heights, and distances. Let’s take an example to understand how to solve problems using trigonometric values.

Suppose we are given the height of a tree and the angle of elevation from a certain point. We can use trigonometric values to calculate the distance from the tree to that point. The formula for this calculation is:

Distance to the Tree = Height of the Tree / tan (Angle of Elevation)

For example, if the height of the tree is 12m and the angle of elevation is 30 degrees, we can calculate the distance to the tree as follows:

Distance to the Tree = 12 / tan (30) = 12 / 0.58 = 20.69m

Conclusion: Key Takeaways

In conclusion, understanding how to calculate trigonometric values is crucial for solving problems in various fields. Sine, cosine, and tangent are the three main trigonometric values used in these calculations. By learning how to calculate trigonometric values and how to use them to solve problems with given information, we can better understand and analyze complex problems in our work or daily life.