Which expression is equal to cos50^∘ ? A. sin20^∘ cos30^∘+cos20^∘ sin30^∘ B. sin20^∘ cos30^∘-c

Name: Problem 60, Chapter 14: Algebra 2
Uploaded: 2019-08-14T18:30:16-08:00
Duration: 1 min 6 s
Channel: Taylor Shimono
Description: Which expression is equal to cos50^∘ ? A. sin20^∘ cos30^∘+cos20^∘ sin30^∘ B. sin20^∘ cos30^∘-cos20^∘-cos20^∘ sin30^∘ C ·cos20^∘ cos30^∘+sin20^∘ sin30^∘ D. cos20^∘ cos30^∘-sin20^∘ sin30^∘

step 1 So for this problem, we're going to begin by looking at each of our answer choices. And so we se

Question

Which expression is equal to $\cos 50^{\circ} ?$ A. $\sin 20^{\circ} \cos 30^{\circ}+\cos 20^{\circ} \sin 30^{\circ} \quad$ B. $\sin 20^{\circ} \cos 30^{\circ}-\cos 20^{\circ}-\cos 20^{\circ} \sin 30^{\circ}$ $\mathrm{C} \cdot \cos 20^{\circ} \cos 30^{\circ}+\sin 20^{\circ} \sin 30^{\circ} \quad$ D. $\cos 20^{\circ} \cos 30^{\circ}-\sin 20^{\circ} \sin 30^{\circ}$

   Which expression is equal to $\cos 50^{\circ} ?$
A. $\sin 20^{\circ} \cos 30^{\circ}+\cos 20^{\circ} \sin 30^{\circ} \quad$ B. $\sin 20^{\circ} \cos 30^{\circ}-\cos 20^{\circ}-\cos 20^{\circ} \sin 30^{\circ}$
$\mathrm{C} \cdot \cos 20^{\circ} \cos 30^{\circ}+\sin 20^{\circ} \sin 30^{\circ} \quad$ D. $\cos 20^{\circ} \cos 30^{\circ}-\sin 20^{\circ} \sin 30^{\circ}$

Algebra 2

Prentice Hall, Basia… 1st Edition

Chapter 14, Problem 60

Instant Answer

Solved by Expert Taylor Shimono

08/14/2019

Step 1

We can break this down into $\cos (20^{\circ} + 30^{\circ})$. Show more…

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Which expression is equal to $\cos 50^{\circ} ?$ A. $\sin 20^{\circ} \cos 30^{\circ}+\cos 20^{\circ} \sin 30^{\circ} \quad$ B. $\sin 20^{\circ} \cos 30^{\circ}-\cos 20^{\circ}-\cos 20^{\circ} \sin 30^{\circ}$ $\mathrm{C} \cdot \cos 20^{\circ} \cos 30^{\circ}+\sin 20^{\circ} \sin 30^{\circ} \quad$ D. $\cos 20^{\circ} \cos 30^{\circ}-\sin 20^{\circ} \sin 30^{\circ}$

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Key Concepts

Cosine Addition Formula

This formula expresses the cosine of the sum of two angles, stating that cos(A+B) = cos A cos B - sin A sin B. It is essential for combining trigonometric expressions and transforming sums into products, which is particularly useful when needing to match or simplify expressions.

Sine Addition Formula

The sine addition formula states that sin(A+B) = sin A cos B + cos A sin B. It plays a crucial role in expressing the sine of a sum of angles in terms of the sine and cosine of the individual angles, helping in comparisons and transformations of trigonometric expressions.

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