190k views
2 votes
Cos(81°)cos(36) + sin(81°)sin(369) Find the values of α and β. a) α = 81° and β = 36°

b) α = 81° and β = 369°
c) α = 81° and β = -369°
d) α = 81° and β = -36°

1 Answer

2 votes

Final answer:

The correct answer is option d) α = 81° and β = -36°.

Step-by-step explanation:

The correct answer is option d) α = 81° and β = -36°.

To find the values of α and β, we can use the identities cos(a-b) = cos(a)cos(b) + sin(a)sin(b) and sin(a+b) = sin(a)cos(b) + cos(a)sin(b).

Using the given values of cos(81°) = 0.123 and sin(81°) = 0.993, and cos(36°) = 0.809 and sin(36°) = 0.588, we can substitute these values into the identities to find that:

cos(81°)cos(36°) + sin(81°)sin(36°) = 0.123 * 0.809 + 0.993 * 0.588 ≈ 0.099 + 0.583 ≈ 0.682

Therefore, the values of α and β that make the equation true are α = 81° and β = -36°.

The expression given can be simplified using the cosine addition formula: cos(α - β) = cos(α)cos(β) + sin(α)sin(β). Applying this formula, we get cos(81° - 36°) = cos(81°)cos(36°) + sin(81°)sin(36°), which simplifies to cos(45°). Therefore, the values of α and β that make the equality true correspond to option (a).

User Sufuko
by
8.1k points

Related questions

asked Dec 13, 2020 205k views
Intermernet asked Dec 13, 2020
by Intermernet
8.7k points
2 answers
3 votes
205k views