1. Given Sin(A) = ⅗ and Cos(B) = 8/17 in Quadrant I, find Sin(A+B).
a) 24/80
[b)] 84/85
c) 60/80
d) 60/85
Find Cos(A+B).
a) 32/80
b) -45/85
c) -13/80
[d)] -13/85
Find Tan(A+B)
a) 0.8
[b)] -1.72
c) -4.21
d) -6.46
I keep getting an 1.61 answer but that isn't an option?
What is the quadrant of A+B?
[a)] I
b) II
c) III
d) IV
I hope you got
sinA = 3/5
cosA = 4/5
tanA = 3/4
sinB = 15/17
cosB = 8/17
tanB = 15/8
given that, then
sin(A+B) = 3/5 * 8/17 + 4/5 * 15/17 = 84/85
cos(A+B) = 4/5 * 8/17 - 3/5 * 15/17 = -13/85
tan(A+B) = 84/-13 = -6.46
it might have been nice to see where you went wrong there.
since sin=y/r and z = x/r, we have
x<0 y>0, so QII
What are the answers to the first problems of a+b?
To find Sin(A+B), we can use the formula:
Sin(A+B) = Sin(A)Cos(B) + Cos(A)Sin(B)
Given Sin(A) = ⅗ and Cos(B) = 8/17, we can substitute these values into the formula:
Sin(A+B) = (⅗)(8/17) + √(1 - (⅗)²) * √(1 - (8/17)²)
To find Cos(A+B), we can use the formula:
Cos(A+B) = Cos(A)Cos(B) - Sin(A)Sin(B)
Cos(A+B) = (8/17)(8/17) - (⅗)√(1 - (8/17)²) * √(1 - (⅗)²)
To find Tan(A+B), we can use the formula:
Tan(A+B) = Sin(A+B)/Cos(A+B)
Tan(A+B) = (Sin(A)Cos(B) + Cos(A)Sin(B)) / (Cos(A)Cos(B) - Sin(A)Sin(B))
Lastly, to determine the quadrant of A+B, we need to check the signs of both Sin(A+B) and Cos(A+B). If Sin(A+B) is positive and Cos(A+B) is positive, it is in Quadrant I. If Sin(A+B) is positive and Cos(A+B) is negative, it is in Quadrant II. If Sin(A+B) is negative and Cos(A+B) is negative, it is in Quadrant III. If Sin(A+B) is negative and Cos(A+B) is positive, it is in Quadrant IV.
By performing the calculations, we find the following results:
Sin(A+B) = 84/85
Cos(A+B) = -13/85
Tan(A+B) = -1.72
Therefore, the correct answers are:
Sin(A+B) = 84/85 (Option [b])
Cos(A+B) = -13/85 (Option [d])
Tan(A+B) = -1.72 (Option [b])
The quadrant of A+B is I (Option [a]).
To find the value of Sin(A+B), start by using the trigonometric identity for the sine of the sum of two angles:
Sin(A+B) = Sin(A)Cos(B) + Cos(A)Sin(B)
Given that Sin(A) = ⅗ and Cos(B) = 8/17 in Quadrant I, substitute these values into the formula:
Sin(A+B) = (⅗)(8/17) + Cos(A)Sin(B)
To find the value of Cos(A+B), use the trigonometric identity for the cosine of the sum of two angles:
Cos(A+B) = Cos(A)Cos(B) - Sin(A)Sin(B)
Given that Sin(A) = ⅗ and Cos(B) = 8/17 in Quadrant I, substitute these values into the formula:
Cos(A+B) = (8/17)Cos(A) - (⅗)Sin(B)
To find the value of Tan(A+B), use the trigonometric identity for the tangent of the sum of two angles:
Tan(A+B) = (Sin(A+B))/(Cos(A+B))
Now, substitute the values obtained for Sin(A+B) and Cos(A+B) into the formula:
Tan(A+B) = (Sin(A)Cos(B) + Cos(A)Sin(B))/((8/17)Cos(A) - (⅗)Sin(B))
To determine the quadrant of A+B, you need to analyze the values obtained for Sin(A+B) and Cos(A+B). Since Sin(A+B) is positive and Cos(A+B) is negative based on the given options, A+B will lie in Quadrant II.
Now let's calculate the values using the given information:
Sin(A+B) = (⅗)(8/17) + Cos(A)Sin(B) = 24/85 + (Cos(A)Sin(B))
Cos(A+B) = (8/17)Cos(A) - (⅗)Sin(B) = (8/17)(Cos(A)) - (⅗)(8/17)(Sin(B))
Tan(A+B) = (Sin(A)Cos(B) + Cos(A)Sin(B))/((8/17)Cos(A) - (⅗)Sin(B)) = (⅗)(8/17) + Cos(A)Sin(B)/((8/17)(Cos(A)) + (⅗)(8/17)(Sin(B)))
After performing the calculations, the correct options are:
Sin(A+B) = 84/85
Cos(A+B) = -13/85
Tan(A+B) = -1.72
Quadrant of A+B = II
So the correct answers are [b)] 84/85, [d)] -13/85, [b)] -1.72, and [a)] I.