If sin = -3/5 with A in QIV, find cos A/2
If QIV means fourth q
To find the value of cos(A/2), we can use the half-angle identity for cosine:
cos(A/2) = ±sqrt((1 + cos(A)) / 2)
However, before we can use this formula, we need to find the value of cos(A).
Given that sin(A) = -3/5 and A is in the fourth quadrant, we can determine the value of cos(A) using the Pythagorean identity:
sin^2(A) + cos^2(A) = 1
Substituting the value of sin(A) and solving for cos(A):
(-3/5)^2 + cos^2(A) = 1
9/25 + cos^2(A) = 1
cos^2(A) = 1 - 9/25
cos^2(A) = 16/25
cos(A) = ±sqrt(16/25)
cos(A) = ±4/5
Since A is in the fourth quadrant, cos(A) is positive (as the cosine value is positive in the fourth quadrant).
Now, we can substitute the value of cos(A) into the half-angle identity for cosine:
cos(A/2) = ±sqrt((1 + cos(A)) / 2)
cos(A/2) = ±sqrt((1 + 4/5) / 2)
cos(A/2) = ±sqrt((9/5)/2)
cos(A/2) = ±sqrt(9/10)
cos(A/2) = ±3/√10
Therefore, cos(A/2) has two possible values: 3/√10 or -3/√10, depending on the sign chosen.