2) Suppose sinA = 12/13 with 90º≤A≤180º. Suppose also that sinB = -7/25 with -90º≤B≤0º. Find cos(A + B).
3)
Suppose sinA = 12/13 with 90º≤A≤180º. Suppose also that sinB = -7/25 with -90º≤B≤0º. Find cos(A - B).
+23254 cos(A + B) = cosA·cosB - sinA·sinB
Angle A is in the second quadrant. Draw the diagram! Using the quadratic formula, the missing side has length 5. Because it's in the second quadrant, x = -5, y = 12, hypotenuse = 13. sinA = 12/13, cosA = -5/13
Angle B is in the fourth quadranta. Draw the diagram! Using the quadratic formula, the missing side has length 24. Because it in the fourth quadrant, x = 24, y = -7, hypotenuse = 25. sinB = -7/24, cosB = 24/25.
Place these values into the formula for cos(A + B) to get the answer.
+23254 cos(A + B) = cosA·cosB - sinA·sinB
Angle A is in the second quadrant. Draw the diagram! Using the quadratic formula, the missing side has length 5. Because it's in the second quadrant, x = -5, y = 12, hypotenuse = 13. sinA = 12/13, cosA = -5/13
Angle B is in the fourth quadranta. Draw the diagram! Using the quadratic formula, the missing side has length 24. Because it in the fourth quadrant, x = 24, y = -7, hypotenuse = 25. sinB = -7/24, cosB = 24/25.
Place these values into the formula for cos(A + B) to get the answer.
