Find the value of TAN 45 degree and COT 45 degree

Find the value of TAN 45 degree and COT 45 degree

The correct answer and explanation is:

The value of tan 45° and cot 45° can be determined using basic trigonometric relationships:

1. tan 45° = 1
2. cot 45° = 1

Explanation:

To understand why these values are what they are, it’s essential to understand the definitions of tangent and cotangent.

• Tangent (tan) of an angle in a right triangle is the ratio of the opposite side to the adjacent side. For a 45° angle in a right triangle, since both the opposite and adjacent sides are equal, the ratio is 1. Thus, tan 45° = 1.
• Cotangent (cot) is the reciprocal of the tangent function. That means: cot⁡θ=1tan⁡θ\cot \theta = \frac{1}{\tan \theta} So, for cot 45°, since tan 45° = 1, the reciprocal of 1 is also 1. Therefore, cot 45° = 1.

This result can be confirmed by using the unit circle or a right triangle approach. In the unit circle, at 45°, both the sine and cosine functions are equal, and since tangent is the ratio of sine to cosine, it simplifies to 1. Similarly, since cotangent is the reciprocal of tangent, cot 45° is also 1.

Thus, both tan 45° and cot 45° have the value 1.