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10 grade maths

Find the value of sin 75°

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10 Months agoGrade
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1 Answer

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ApprovedApproved Tutor Answer10 Months ago

To find the value of sin 75°, we can use the sine addition formula. This angle can be expressed as the sum of two angles: 45° and 30°.

Sine Addition Formula

The formula is:

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

Applying the Formula

For sin 75°, let:

  • a = 45°
  • b = 30°

Now, we can substitute:

sin 75° = sin(45° + 30°)

Using the values:

  • sin 45° = √2/2
  • cos 45° = √2/2
  • sin 30° = 1/2
  • cos 30° = √3/2

Calculating sin 75°

Now plug these values into the formula:

sin 75° = sin 45° * cos 30° + cos 45° * sin 30°

Substituting the known values:

sin 75° = (√2/2 * √3/2) + (√2/2 * 1/2)

sin 75° = (√6/4) + (√2/4)

Combining these gives:

sin 75° = (√6 + √2) / 4

Final Result

The value of sin 75° is:

sin 75° = (√6 + √2) / 4

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