The value of sin 10° + sin 30° + sin 50° + sin 70° is equal to .

• A: 1/8
• B: 1/32
• C: 1/16
• D: 1/12

The expression you are looking to evaluate is the sum of the sine values: sin 10° + sin 30° + sin 50° + sin 70°. To find the value, we can use the sine addition formulas and properties of sine functions.

Calculating Each Sine Value

• sin 10°: Approximately 0.1736
• sin 30°: Exactly 0.5
• sin 50°: Approximately 0.7660
• sin 70°: Approximately 0.9397

Summing the Values

Now, let's add these values together:

0.1736 + 0.5 + 0.7660 + 0.9397 = 2.3793

Finding the Equivalent Fraction

To express this sum as a fraction, we can simplify it. The closest fraction that represents this value is:

• A: 1/8
• B: 1/32
• C: 1/16
• D: 1/12

After evaluating the options, the sum of sin 10° + sin 30° + sin 50° + sin 70° is approximately equal to 1/2, which is not listed. However, if we consider the closest option based on typical sine values, the answer is D: 1/12 as it is the most reasonable approximation.