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dimaraw [331]
2 years ago
11

If a and b are two angles in standard position in Quadrant I, find cos(a+b) for the given function values. sin a=8/17and cos b=1

2/13
1) -220/221

2) -140/221

3) 140/221

4) 220/221
Mathematics
1 answer:
n200080 [17]2 years ago
6 0

Recall the sum identity for cosine:

cos(a + b) = cos(a) cos(b) - sin(a) sin(b)

so that

cos(a + b) = 12/13 cos(a) - 8/17 sin(b)

Since both a and b terminate in the first quadrant, we know that both cos(a) and sin(b) are positive. Then using the Pythagorean identity,

cos²(a) + sin²(a) = 1   ⇒   cos(a) = √(1 - sin²(a)) = 15/17

cos²(b) + sin²(b) = 1   ⇒   sin(b) = √(1 - cos²(b)) = 5/13

Then

cos(a + b) = 12/13 • 15/17 - 8/17 • 5/13 = 140/221

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1.

16² + b² = 17²

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256 - 256 + b² = 289 - 256

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√b² = √33

b = 5.74 or 5.7

2.

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3.

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49 + 81 = c²

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√130 = √c²

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4.

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6.

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