Section 1: find the sine, cosine, and tangent ratios of ∠x.

section 2: find the sine, cosine, and tangent ratios of ∠y.

section 3: using your answers from parts 1 and 2, what is significant about the sin∠x and the cos∠y?

section 4: using your answer from parts 1 and 2, how are the tangents of ∠x and ∠y related to each other?

Section 1.

sin∠X =5/13

cos∠X =12/13

tan∠X = 5/12

Step-by-step explanation:

The sine of an angle is defined as; Opposite side/the Hypotenuse. From the right angle triangle given; the opposite side of angle X is 5 while the hypotenuse is 13.

The cosine of an angle is defined as; Adjacent side/Hypotenuse. From the right angle triangle given; the adjacent side of angle X is 12.

The tangent of an angle is defined as; Opposite side/Adjacent side.

Section 2

sin∠Y = 12/13

cos∠Y = 5/13

tan∠Y = 12/5

Step-by-step explanation:

The sine of an angle is defined as; Opposite side/the Hypotenuse. From the right angle triangle given; the opposite side of angle Y is 12 while the hypotenuse is 13.

The cosine of an angle is defined as; Adjacent side/Hypotenuse. From the right angle triangle given; the adjacent side of angle Y is 5.

The tangent of an angle is defined as; Opposite side/Adjacent side.

Section 3

The sin∠X and the cos∠Y are equal, their value is 5/13.

Step-by-step explanation:

The sine of angle is always equal to the cosine of its complement. Complement angles add up to 90 degrees. In this case, ∠X+∠Y =90 hence ∠X is a complement of ∠Y.

Section 4

The tangents of ∠X and ∠Y are reciprocals of each other. That is;

tan∠X = 5/12 and tan∠Y = 12/5. Clearly; tan∠Y = 1/tan∠X .

Step-by-step explanation:

The tangent of an angle will always be equal to the reciprocal of the tangent of its complement. In this case, ∠X+∠Y =90 hence ∠X is a complement of ∠Y.

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