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

question 46

Multiple Choice

Use the trigonometric substitution to rewrite the algebraic expression as a trigonometric function of θ,where $- \frac { \pi } { 2 } < \theta < \frac { \pi } { 2 }$ .Then find sin θ and cos θ.​ $4 = \sqrt { 64 - x ^ { 2 } } , x = 8 \sin \theta$

• A)​ \(64 \sin \theta = 4 ; \sin \theta = \pm \frac { \sqrt { 3 } } { 2 } ; \cos \theta = \frac { 1 } { 2 }\)
• B)​ \(64 \cos \theta = 4 ; \sin \theta = \pm \frac { \sqrt { 3 } } { 2 } ; \cos \theta = \frac { 1 } { 2 }\)
• C)​ \(8 \sin \theta = 4 ; \sin \theta = \pm \frac { \sqrt { 3 } } { 2 } ; \cos \theta = \frac { 1 } { 2 }\)
• D)​ \(8 \cos \theta = 4 ; \sin \theta = \pm \frac { \sqrt { 3 } } { 2 } ; \cos \theta = \frac { 1 } { 2 }\)
• E)​ \(8 \cos \theta = 4 ; \sin \theta = \frac { 1 } { 2 } ; \cos \theta = \pm \frac { \sqrt { 3 } } { 2 }\)

---

Definitions:

Myocardial Infarction

A medical emergency commonly known as a heart attack, caused by the interruption of blood flow to a part of the heart, leading to heart muscle damage.

Cardiovascular Disease

Cardiovascular disease refers to a class of diseases that involve the heart or blood vessels, including coronary artery disease, heart failure, and stroke.

Glucose Metabolism

The series of biochemical processes by which cells produce, utilize, and regulate glucose for energy and cellular functions.

Circulating Lipids

Fats or fat-like substances found in the blood, which include cholesterol and triglycerides, playing crucial roles in energy storage and cell structure.