Determine the sine of the product of 17/32×-1/10
To find the sine of the product (\(\sin(A \cdot B)\)) of two angles, we can use the sine of the sum identity:
\[\sin(A \cdot B) = \sin(A) \cos(B) + \cos(A) \sin(B)\]
In this case, we have:
\[A = \frac{17}{32} \quad \text{and} \quad B = -\frac{1}{10}\]
First, we find \(\sin(A)\) and \(\cos(A)\):
Using the sine of the angle formula, we have:
\[\sin(A) = \sin\left(\frac{17}{32}\right)\]
Using the cosine of the angle formula, we have:
\[\cos(A) = \cos\left(\frac{17}{32}\right)\]
Next, we find \(\sin(B)\) and \(\cos(B)\):
Using the sine of the angle formula, we have:
\[\sin(B) = \sin\left(-\frac{1}{10}\right)\]
Using the cosine of the angle formula, we have:
\[\cos(B) = \cos\left(-\frac{1}{10}\right)\]
Finally, we can calculate the sine of the product:
\[\sin\left(\frac{17}{32} \cdot -\frac{1}{10}\right) = \sin(A \cdot B) = \sin(A) \cos(B) + \cos(A) \sin(B)\]
To determine the sine of the product of two numbers, we first need to find the product of the two fractions and then find the sine of that product.
Step 1: Multiply the fractions 17/32 and -1/10.
(17/32) * (-1/10) = -17/320
Step 2: Find the sine of -17/320.
The sine function gives the ratio of the length of the opposite side to the length of the hypotenuse in a right triangle. Since -17/320 is a number and not an angle, we cannot directly find the sine value.
Please let me know if you have any further questions.