Question

Sin(0.5x -30°)=cosx for 0∠x ∠90°

Answer 1

Answer:

  x = 80°

Step-by-step explanation:

The relationship between sine and cosine can be written as ...

  cos(x) = sin(90° +x)

So, we can rewrite the given equation as ...

  sin(0.5x -30°) = sin(x +90°)

Taking the inverse sine function of both sides, we get two equations:

• 0.5x -30° = x +90°
• 0.5x -30° = 180° -(x +90°)

because the sine of an angle is also equal to the sine of its supplement.

Solving the first of these equations gives ...

  -120° = 0.5x   ⇒   x = -240° . . . . not in the desired domain

The second of these equations gives ...

  1.5x = 120°   ⇒   x = 80° . . . . . the solution we seek

The solution is x = 80°.

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Check

Filling in the value for x gives ...

  sin(80°/2 -30°) = cos(80°) . . . . true

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A graphing calculator confirms this result.