Recognize Identity: Recognize that the expression sin(15+15) can be rewritten using the angle sum identity for sine. The angle sum identity for sine is sin(A + B) = sin(A)cos(B) + cos(A)sin(B). Here, A and B are both 15 degrees, so we can apply the identity.Apply Identity: Apply the angle sum identity for sine to the expression sin(15+15). sin(15+15) = sin(15)cos(15) + cos(15)sin(15)Calculate Values: Recognize that sin(15) and cos(15) need to be calculated or looked up, as they are not standard angles. However, we know that sin(30) is a standard angle and its value is 1/2. Since 15+15 equals 30, we can simplify the expression to sin(30).Find Expression Value: Use the known value of sin(30) to find the value of the expression. sin(30) = 1/2

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$\sin (15+15)=$

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Math Problems

Grade 8

Multiply using the distributive property

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\sin (15+15)=

Recognize Identity: Recognize that the expression $\sin(15+15)$ can be rewritten using the angle sum identity for sine. The angle sum identity for sine is $\sin(A + B) = \sin(A)\cos(B) + \cos(A)\sin(B)$ . Here, $A$ and $B$ are both $15$ degrees, so we can apply the identity.
Apply Identity: Apply the angle sum identity for sine to the expression $\sin(15+15)$ . $\sin(15+15) = \sin(15)\cos(15) + \cos(15)\sin(15)$
Calculate Values: Recognize that $\sin(15)$ and $\cos(15)$ need to be calculated or looked up, as they are not standard angles. However, we know that $\sin(30)$ is a standard angle and its value is $\frac{1}{2}$ . Since $15+15$ equals $30$ , we can simplify the expression to $\sin(30)$ .
Find Expression Value: Use the known value of $\sin(30)$ to find the value of the expression. $\sin(30) = \frac{1}{2}$