Question 890647
the relationships are as follows:
see the diagram at the bottom.


sin(A) = y/z


cos(A) = x/z


tan(A) = y/x


cot(A) = 1/tan(A) = x/y


sec(A) = 1/cos(A) = z/x


csc(A) = 1/sin(a) = z/y


you are given that cot(A) is equal to 9


that means that cot(a) = x/y = 9/1 which means that x is equal to 9 and y is equal to 1.


the pythagorean theorem states that z^2 = x^2 + y^2.


that means that z^2 = 9^2 + 1^2 which means that z^2 = 82.


that means that z = sqrt(82)


you have:


x = 9
y = 1
z = sqrt(82)


plug these numbers into your equations and  you should get the answer you are looking for after you follow the rules for simplification.


you will get:


sin(A) = y/z = 1 / sqrt(82) = sqrt(82) / 82


cos(A) = x/z = 9 / sqrt(82) = (9 * sqrt(82) / 82


tan(A) = y/x = 1 / 9


cot(A) = 1/tan(A) = x/y = 9 / 1 = 9


sec(A) = 1/cos(A) = z/x = sqrt(82) / 9


csc(A) = 1/sin(a) = z/y = sqrt(82) / 1 = sqrt(82)


here's a picture of your triangle.


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