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The point (-2,5) is on the terminal arm of angle B. Which is the set of exact primary trigonometric ratios for the angle?

(A question about the specific angle and ratios would need to be provided for options)
A) Sine, cosine, and tangent
B) Secant, cosecant, and cotangent
C) Tangent, secant, and cosecant
D) Cotangent, cosine, and sine

1 Answer

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Final answer:

The set of exact primary trigonometric ratios for angle B, given the coordinates of the point (-2,5) on its terminal arm, is sine, cosine, and tangent.

Step-by-step explanation:

The point (-2,5) is on the terminal arm of angle B. To determine the set of exact primary trigonometric ratios for angle B, we need to refer to the coordinates (-2,5) in the right triangle and use the definitions of the trigonometric ratios. Since the point (-2,5) is in the second quadrant, both the x-coordinate and y-coordinate are negative. Therefore, the opposite side is 5 units and the adjacent side is -2 units.

We can use these lengths to find the values of the primary trigonometric ratios for angle B. The primary trigonometric ratios include sine, cosine, and tangent. The sine ratio is equal to the ratio of the opposite side to the hypotenuse, the cosine ratio is equal to the ratio of the adjacent side to the hypotenuse, and the tangent ratio is equal to the ratio of the opposite side to the adjacent side.

In this case, the sine of angle B is 5/h, the cosine of angle B is -2/h, and the tangent of angle B is 5/-2. Therefore, the set of exact primary trigonometric ratios for angle B is sine, cosine, and tangent (A).

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