Use Identities to Solve Trigonometric Equations
Solve the Equation on the Interval

question 166

Multiple Choice

Use Identities to Solve Trigonometric Equations
Solve the equation on the interval [0, 2π) .
- $\sin \left( x + \frac { 5 \pi } { 4 } \right) + \sin \left( x - \frac { 5 \pi } { 4 } \right) = 1$

• A) \(\frac { 5 \pi } { 4 } , \frac { 7 \pi } { 4 }\)
• B) \(\frac { 3 \pi } { 2 } , 3 \pi\)
• C) \(\frac { 3 \pi } { 4 } , \frac { 5 \pi } { 6 }\)
• D) \(\frac { 5 \pi } { 4 } , \frac { 5 \pi } { 6 }\)

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Definitions:

Cognitive Restructuring

A psychotherapeutic process of learning to identify and dispute irrational or maladaptive thoughts known as cognitive distortions, a core aspect of cognitive-behavioral therapy.

Thought Record

A cognitive behavioral therapy tool used to capture, evaluate, and challenge negative thought patterns.

Fear Hierarchy

A fear hierarchy is a list of feared situations or objects that are arranged in descending order according to how much they evoke anxiety. This list is then used in therapy for exposure exercises.

Response Prevention

A behavioral treatment technique, particularly used in treating OCD, where the patient is prevented from performing a compulsive behavior.