key term - ±

Definition

The symbol '±' is used to indicate a positive or negative value, typically representing a range or margin of error. It is commonly encountered in the context of trigonometric functions, particularly in the discussion of double-angle, half-angle, and reduction formulas.

5 Must Know Facts For Your Next Test

1. The '±' symbol indicates that a value can be either positive or negative, allowing for two possible solutions or outcomes.
2. In the context of double-angle formulas, the '±' symbol is used to represent the positive or negative nature of the trigonometric functions for the double angle.
3. Half-angle formulas also utilize the '±' symbol to account for the positive or negative nature of the trigonometric functions for the half-angle.
4. Reduction formulas may employ the '±' symbol to capture the ambiguity in the sign of the trigonometric functions when reducing an angle to a smaller reference angle.
5. Understanding the role of the '±' symbol is crucial in applying and manipulating trigonometric identities, particularly in the context of double-angle, half-angle, and reduction formulas.

Review Questions

• Explain the purpose of the '±' symbol in the context of double-angle formulas.
  • The '±' symbol in double-angle formulas is used to represent the fact that the trigonometric functions of the double angle can be either positive or negative. This allows for two possible solutions or outcomes when applying the double-angle formulas. For example, the formula $\sin(2x) = \pm 2\sin(x)\cos(x)$ indicates that the sine of the double angle can be either positive or negative, depending on the value of the original angle 'x'.
• Describe how the '±' symbol is utilized in half-angle formulas.
  • In half-angle formulas, the '±' symbol is used to account for the positive or negative nature of the trigonometric functions for the half-angle. This is necessary because the sign of the trigonometric functions can change when taking the half-angle of a given angle. For instance, the formula $\sin(\frac{x}{2}) = \pm \sqrt{\frac{1-\cos(x)}{2}}$ shows that the sine of the half-angle can be either positive or negative, depending on the value of the original angle 'x'.
• Analyze the role of the '±' symbol in reduction formulas and its significance in trigonometric identities.
  • Reduction formulas employ the '±' symbol to capture the ambiguity in the sign of the trigonometric functions when reducing an angle to a smaller reference angle. This is important because the sign of the trigonometric functions can change depending on the quadrant of the original angle. The '±' symbol allows for the formulas to be applied correctly, regardless of the quadrant. Understanding the use of the '±' symbol in reduction formulas is crucial for manipulating trigonometric identities and solving problems involving angle reduction.

Related terms

Double-Angle Formulas:

Trigonometric identities that express the sine, cosine, and tangent of a double angle in terms of the original angle.

Half-Angle Formulas:

Trigonometric identities that express the sine, cosine, and tangent of half an angle in terms of the original angle.

Reduction Formulas: Trigonometric identities that express the sine, cosine, and tangent of an angle in terms of the sine, cosine, and tangent of a smaller angle.