To solve the equation \( 2 \tan(x) + 3 = 1 \) for \( x \) in degrees:

1. Start by isolating \( \tan(x) \):
   \[
   2 \tan(x) + 3 = 1
   \]
   Subtract 3 from both sides:
   \[
   2 \tan(x) = 1 - 3 = -2
   \]
   Divide both sides by 2:
   \[
   \tan(x) = \frac{-2}{2} = -1
   \]

2. Now solve for \( x \) by taking the inverse tangent (arctangent):
   \[
   x = \tan^{-1}(-1)
   \]

3. Since \( \tan(x) = -1 \), the basic angle where tangent equals \( -1 \) is \( 135^\circ \) (in the second quadrant, where tangent is negative).

4. However, because the tangent function repeats every 180°, we find the general solutions:
   \[
   x = 135^\circ + 180^\circ n
   \]
   where \( n \) is any integer.

5. The principal solution in the range \( 0^\circ \leq x < 360^\circ \) are:
   \[
   x = 135^\circ \quad \text{and} \quad x = 315^\circ
   \]

Thus, the solutions to \( 2 \tan(x) + 3 = 1 \) in degrees are:
\[
x = 135^\circ \quad \text{or} \quad x = 315^\circ
\]

Would you like more details or have any questions? Here are 5 related questions you might want to explore:

1. How can we solve similar equations involving other trigonometric functions?
2. What are the different methods to solve trigonometric equations?
3. How do we determine the general solution for trigonometric equations?
4. Why does the tangent function repeat every 180 degrees?
5. How can we convert radians to degrees for trigonometric solutions?

**Tip:** Always check the interval you're asked to find solutions in when solving trigonometric equations!

Learn how to solve the trigonometric equation 2 tan(x) + 3 = 1 in degrees with a step-by-step explanation. This problem covers key concepts such as the tangent function, inverse trigonometric functions, and periodicity. Suitable for students in Grades 10-12.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation