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lesya [120]
3 years ago
5

For 0° ≤ x < 360°, what are the solutions to sin(StartFraction x Over 2 EndFraction) + cos(x) – 1 = 0 ?

Mathematics
1 answer:
nataly862011 [7]3 years ago
6 0

Answer:

{60°,300°}

b.

Step-by-step explanation:

edge 2020

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kolbaska11 [484]

Answer:

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Step-by-step explanation:

There are a couple of ways to go at these. One is to use the sum and difference formulas for the cosine and sine functions. To do that, you need to find the sine for the angle whose cosine is given, and vice versa.

Another approach is to use the inverse trig functions to find the angles α and β, then combine those angles and find find the desired function of the combination.

For the first problem, we'll do it the first way:

  sin(α) = √(1 -cos²(α)) = √(1 -.926²) = √0.142524 ≈ 0.377524

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__

a) cos(α+β) = cos(α)cos(β) -sin(α)sin(β)

  = 0.926×0.993820 -0.377524×0.111

  cos(α+β) ≈ 0.8784

__

b) sin(β -α) = sin(arcsin(0.111) -arccos(0.926)) ≈ sin(6.3730° -22.1804°)

  = sin(-15.8074°)

  sin(β -α) ≈ -0.2724

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4 years ago
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