What is the value of tan(-135) and also cot(-135)..? Solve by writing the steps.

To find the values of tan(-135°) and cot(-135°), we can use the properties of trigonometric functions and their relationship to the unit circle. Let's break down the steps clearly.

Finding tan(-135°)

First, we need to understand that tan is a periodic function. The tangent function has a period of 180°, which means:

• tan(θ) = tan(θ + 180°n) for any integer n.

Given that -135° is negative, we can convert it to a positive angle by adding 180°:

-135° + 180° = 45°.

Now, we can express tan(-135°) as:

tan(-135°) = tan(45°).

From trigonometric values, we know:

• tan(45°) = 1.

Therefore, we conclude:

tan(-135°) = 1.

Calculating cot(-135°)

The cotangent function is the reciprocal of the tangent function, which means:

cot(θ) = 1/tan(θ).

Using the value we just found:

cot(-135°) = 1/tan(-135°) = 1/1 = 1.

Thus, we can summarize:

cot(-135°) = 1.

Summary of Results

In summary, the values we calculated are:

• tan(-135°) = 1
• cot(-135°) = 1

This method of using the periodic properties of trigonometric functions helps us simplify calculations, especially when dealing with negative angles. Understanding the unit circle and the behavior of these functions can make it much easier to solve similar problems in the future!