Stumped on this question - please explain!
If sin A = 0.35, cos A = 0.94, sin B = 0.58, and cos B = 0.81, what is sin(A + B)?
Am I just plugging the values into sin(A + B) or do I have to do more than that? Thank you.
To find sin(A + B), you will need to use the trigonometric identity known as the sum formula for sine. The sum formula for sine states that sin(A + B) = sin A * cos B + cos A * sin B.
Here are the steps to find sin(A + B) using the given values:
Step 1: Substitute the given values into the sum formula for sine.
sin(A + B) = (sin A * cos B) + (cos A * sin B)
Step 2: Substitute the given values of sin A, cos A, sin B, and cos B into the equation.
sin(A + B) = (0.35 * 0.81) + (0.94 * 0.58)
Step 3: Simplify the expression.
sin(A + B) = 0.2835 + 0.5452
Step 4: Add the two values to get the final answer.
sin(A + B) ≈ 0.8287
Therefore, sin(A + B) is approximately 0.8287.
To find the value of sin(A + B), we can use a trigonometric identity known as the sum formula for sine. The sum formula states that sin(A + B) = sin(A) * cos(B) + cos(A) * sin(B).
In this case, you have the values of sin A, cos A, sin B, and cos B given. To find sin(A + B), we need to plug these values into the sum formula.
So, we can substitute sin A = 0.35, cos A = 0.94, sin B = 0.58, and cos B = 0.81 into the formula and calculate:
sin(A + B) = sin(A) * cos(B) + cos(A) * sin(B)
= (0.35) * (0.81) + (0.94) * (0.58)
Let's simplify the expression:
sin(A + B) = 0.2835 + 0.5452
= 0.8287
Therefore, sin(A + B) ≈ 0.8287.
you need to review your sum of angles formula:
sin(A+B) = sinA cosB + cosA sinB
Now just plug and chug