SOLUTION: Sketch a right triangle corresponding to the trigonometric function of the acute angle θ. Use the Pythagorean Theorem to determine the third side and then find the other five

Algebra ->  Trigonometry-basics -> SOLUTION: Sketch a right triangle corresponding to the trigonometric function of the acute angle θ. Use the Pythagorean Theorem to determine the third side and then find the other five       Log On


   

Question 890647: Sketch a right triangle corresponding to the trigonometric function of the acute angle θ. Use the Pythagorean Theorem to determine the third side and then find the other five trigonometric functions of θ.
cot θ = 9
Answer by Theo(13342) About Me  (Show Source):
You can put this solution on YOUR website!
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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