Use Identities to Write the Expression as a Single Function $$\theta$$

question 283

Multiple Choice

Use identities to write the expression as a single function of x or $$\theta$$
- $\sin \left( \frac { \pi } { 4 } - x \right)$

• A) \(\sin x\)
• B) \(\frac { \sqrt { 2 } } { 2 } \cos x - \frac { \sqrt { 2 } } { 2 } \sin x\)
• C) \(\frac { \sqrt { 2 } } { 2 } \cos x + \frac { \sqrt { 2 } } { 2 } \sin x\)
• D) \(- \cos x\)

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Definitions:

Chemical Shift

In nuclear magnetic resonance (NMR) spectroscopy, a measure of the difference in resonant frequency of a nuclear spin relative to a standard.

Sensitivity

The degree to which a system or a measurement responds to a change in a given variable, commonly used in contexts ranging from scientific instruments to personal perception.

Proton Spin Decoupled

A technique in NMR spectroscopy where the interaction between proton spins is removed to simplify the spectrum.

Carbonyl Carbon

The carbon atom that is part of the carbonyl group (C=O), key in various organic compounds like ketones and aldehydes.