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Simplify J25 sin² (t) +25c05² (+)

Simplify J25 sin² (t) +25c05² (+)

Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter1: Fundamental Concepts Of Algebra
Section: Chapter Questions
Problem 35RE
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### Simplify the Expression Given the following expression, we aim to simplify it: \[ \sqrt{25\sin^2(t) + 25\cos^2(t)} \] #### Step-by-Step Simplification: 1. **Factor out the common term**: \[ \sqrt{25(\sin^2(t) + \cos^2(t))} \] 2. **Use the Pythagorean identity**: \[ \sin^2(t) + \cos^2(t) = 1 \] Applying this identity, the expression simplifies to: \[ \sqrt{25 \cdot 1} \] 3. **Simplify further**: \[ \sqrt{25} = 5 \] Therefore, the simplified form of the expression is: \[ 5 \] ### Conclusion The given expression \[ \sqrt{25\sin^2(t) + 25\cos^2(t)} \] simplifies to 5. By recognizing and applying the Pythagorean identity, the simplification process becomes straightforward, highlighting a fundamental aspect of trigonometric identities.
Transcribed Image Text:### Simplify the Expression Given the following expression, we aim to simplify it: \[ \sqrt{25\sin^2(t) + 25\cos^2(t)} \] #### Step-by-Step Simplification: 1. **Factor out the common term**: \[ \sqrt{25(\sin^2(t) + \cos^2(t))} \] 2. **Use the Pythagorean identity**: \[ \sin^2(t) + \cos^2(t) = 1 \] Applying this identity, the expression simplifies to: \[ \sqrt{25 \cdot 1} \] 3. **Simplify further**: \[ \sqrt{25} = 5 \] Therefore, the simplified form of the expression is: \[ 5 \] ### Conclusion The given expression \[ \sqrt{25\sin^2(t) + 25\cos^2(t)} \] simplifies to 5. By recognizing and applying the Pythagorean identity, the simplification process becomes straightforward, highlighting a fundamental aspect of trigonometric identities.
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