Use the Trigonometric Substitution to Rewrite the Algebraic Expression as a Trigonometric

question 27

Multiple Choice

Use the trigonometric substitution to rewrite the algebraic expression as a trigonometric function of θ,where $- \frac { \pi } { 2 } < x < \frac { \pi } { 2 }$ .Then find sin θ and cos θ. $4 = \sqrt { 16 - x ^ { 2 } } , x = 4 \sin \theta$

• A) \(16 \cos \theta = 4 ; \sin \theta = 0 ; \cos \theta = 1\)
• B)​ \(4 \cos \theta = 4 ; \sin \theta = 0 ; \cos \theta = 1\)
• C)​ \(16 \sin \theta = 4 ; \sin \theta = 0 ; \cos \theta = 1\)
• D)​ \(4 \cos \theta = 4 ; \sin \theta = 1 ; \cos \theta = 0\)
• E)​ \(4 \sin \theta = 4 ; \sin \theta = 0 ; \cos \theta = 1\)

---

Definitions:

Social Cognition

The process of perceiving, interpreting, and processing information about the social world and its inhabitants.

Tight-knit Groups

Social groups characterized by close relationships among members, shared values, and often a sense of unity and loyalty.

Same-gender Relationships

Romantic, sexual, or emotional attractions and relationships between individuals of the same gender, encompassing both identity and behavior.

Cognitive Miser

A theory suggesting that humans, aiming to reduce mental effort, rely on simple and cost-efficient strategies rather than on more sophisticated and effortful processing.