i am homeschooled so i don't really have a teacher teaching me one on one. so most of my help comes from here.thnks..can anyone help me on this.
use identities to find the indicated function value.
secA=5/4 and A in quadrant IV. Find tan A.
A. -sqrt9/5
B. -sqrt9/4
C. -sqrt5/4
D. -sqrt9
if the sec is 5/4
then the cos is 4/5
This is a three, four, five right triangle in the fourth quadrant, so the sin is -3/5
tan = sin /cos = -3/4 which is -sqrt 9 /4
thnks
Of course, I'm happy to help you with this math problem!
To find the value of tan A when sec A is given, we can use the identity: sec^2 A = 1 + tan^2 A.
In this case, sec A is given as 5/4. We can square both sides of the equation to isolate the tan^2 A term:
(sec A)^2 = (5/4)^2
1 + tan^2 A = 25/16
Now we can solve for tan A. Rearranging the equation:
tan^2 A = 25/16 - 1
tan^2 A = 25/16 - 16/16
tan^2 A = 9/16
Taking the square root of both sides:
tan A = ±√(9/16)
Since we are given that A is in quadrant IV, where tan A is negative, we can eliminate the positive root.
Therefore, tan A = -√(9/16). Now simplify the expression:
tan A = -√9/√16
tan A = -3/4
So, the correct answer is D. -sqrt9.
Remember, when using trigonometric identities, it's important to have a solid understanding of the identities and how they can be manipulated to solve for unknowns.