If sin A=-7/25 and angle A terminates in Quadrant IV, cos A equals..
A. -24/25
B. -7/24
C. 24/25
D. 7/24
PLEASE HELP
To find cos A, we can use the Pythagorean identity: sin^2 A + cos^2 A = 1.
Given that sin A = -7/25, we can substitute this value into the equation:
(-7/25)^2 + cos^2 A = 1
Simplifying, we get:
49/625 + cos^2 A = 1
Subtracting 49/625 from both sides, we have:
cos^2 A = 576/625
Taking the square root of both sides, we find:
cos A = ± √(576/625)
Since angle A terminates in Quadrant IV, which is the right side of the x-axis, the value of cos A should be positive. Thus, cos A = √(576/625).
Simplifying further:
cos A = √(24^2/25^2) = 24/25
Therefore, the correct answer is A. -24/25.
To find the value of cos A, we can use the Pythagorean identity sin^2(A) + cos^2(A) = 1.
Given that sin A = -7/25, we can find cos A as follows:
1. First, square the value of sin A: (-7/25)^2 = 49/625.
2. Substitute this value into the Pythagorean identity: 49/625 + cos^2(A) = 1.
3. Solve for cos^2(A) by subtracting 49/625 from both sides: cos^2(A) = 1 - 49/625.
4. Simplify the expression on the right side: cos^2(A) = 576/625.
5. Take the square root of both sides to find cos A: cos A = ±√(576/625).
Since angle A terminates in Quadrant IV, we know that cosine is positive in Quadrant IV. Therefore, cos A is positive.
6. Simplify the expression further: cos A = √(576/625) = 24/25.
So, the answer is C. 24/25.
X^2 + Y^2 = 25^2, X^2 + (-7)^2 = 625, X^2 = 625-49 = 576, X = 24.
Cos A = x/r = 24/25.