sin 12° + sin 48° + sin 54° is equal to

• A) 1/16
• B) 1/32
• C) 1/8
• D) 1/4

To solve the expression sin 12° + sin 48° + sin 54°, we can use some trigonometric identities and properties.

Using Angle Relationships

First, notice that sin 54° can be rewritten using the identity sin(90° - x) = cos(x):

• sin 54° = cos 36°

Combining the Sines

Now, we can rewrite the expression:

• sin 12° + sin 48° + cos 36°

Calculating Values

Next, we can find the approximate values of these sines and cosine:

• sin 12° ≈ 0.2079
• sin 48° ≈ 0.7431
• cos 36° ≈ 0.8090

Adding Them Up

Now, let's add these values together:

• 0.2079 + 0.7431 + 0.8090 ≈ 1.7600

Finding the Equivalent Fraction

To express this sum as a fraction, we can look for a common denominator. The closest option from the choices given is:

• D) 1/4

Thus, the answer to sin 12° + sin 48° + sin 54° is approximately equal to 1/4.