Math Problem Statement

What is the angle θ such that 2sin(θ) = 1?

Solution

The image provided contains partially obscured text, but I will attempt to extract as much useful information as possible.

From what I can interpret, the text mentions:

  • Something involving an angle and a specific trigonometric ratio.
  • A mathematical expression involving sin(θ)\sin(\theta), with a possible equation of 2sin(θ)=12 \sin(\theta) = 1.
  • A request to calculate the angle θ\theta.

Based on the partial equation 2sin(θ)=12 \sin(\theta) = 1, we can proceed to solve for θ\theta.

Solution:

  1. Divide both sides of the equation by 2: sin(θ)=12\sin(\theta) = \frac{1}{2}

  2. The angle θ\theta whose sine is 12\frac{1}{2} corresponds to: θ=30 or θ=150\theta = 30^\circ \text{ or } \theta = 150^\circ in degrees (using the principal values of sine).

Would you like further clarification or any additional details on solving trigonometric equations?

Here are some related questions:

  1. What are the other trigonometric functions (cosine, tangent) for these angles?
  2. How do we find angles in radians from sine values?
  3. What is the general solution for sin(θ)=12\sin(\theta) = \frac{1}{2}?
  4. How do inverse trigonometric functions work in solving such equations?
  5. How does this solution relate to unit circle concepts?

Tip: Remember that sine functions repeat every 360360^\circ (or 2π2\pi radians), so solutions can have multiple forms!

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Math Problem Analysis

Mathematical Concepts

Trigonometry
Solving Trigonometric Equations

Formulas

sin(θ) = 1/2

Theorems

Trigonometric functions and their principal values

Suitable Grade Level

Grades 10-12