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"Find the values of the six trigonometric functions for each angle A in standard position if the point (16, 30) lies on its terminal side.

User Vic V
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Final answer:

To find the values of the six trigonometric functions for angle A, we need to find the ratios of the sides of the triangle formed by the point (16, 30), the x-axis, and the hypotenuse.

Step-by-step explanation:

To find the values of the six trigonometric functions for angle A, we need to find the ratios of the sides of the triangle formed by the point (16, 30), the x-axis, and the hypotenuse. Since the point lies on the terminal side of angle A, we can use the x-coordinate (16) as the adjacent side and the y-coordinate (30) as the opposite side. The hypotenuse can be found using the Pythagorean theorem: hypotenuse = sqrt(adjacent^2 + opposite^2).

Once we have the values of the adjacent, opposite, and hypotenuse, we can calculate the six trigonometric functions:

  • Sine (sin A) = opposite / hypotenuse
  • Cosine (cos A) = adjacent / hypotenuse
  • Tangent (tan A) = opposite / adjacent
  • Cosecant (csc A) = 1 / sin A
  • Secant (sec A) = 1 / cos A
  • Cotangent (cot A) = 1 / tan A

Substituting the values, we get the six trigonometric functions for angle A.

User Krul
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