question 29 (1 point)\nthe point (3,4) is on the terminal arm of ∠a. which is the set of exact primary…

question 29 (1 point)\nthe point (3,4) is on the terminal arm of ∠a. which is the set of exact primary trigonometric ratios for the angle?\n a) sin a = 3/5, cos a = 4/5, tan a = 3/4\n b) sin a = 5/4, cos a = 5/3, tan a = 3/4\n c) sin a = 4/5, cos a = 3/5, tan a = 4/3\n d) sin a = 4/5, cos a = 3/5, tan a = 4/3

question 29 (1 point)\nthe point (3,4) is on the terminal arm of ∠a. which is the set of exact primary trigonometric ratios for the angle?\n a) sin a = 3/5, cos a = 4/5, tan a = 3/4\n b) sin a = 5/4, cos a = 5/3, tan a = 3/4\n c) sin a = 4/5, cos a = 3/5, tan a = 4/3\n d) sin a = 4/5, cos a = 3/5, tan a = 4/3

Answer

Explanation:

Step1: Calculate the hypotenuse ( r )

For a point ((x,y)=(3,4)) on the terminal arm of an angle, use the formula ( r=\sqrt{x^{2}+y^{2}} ). ( r = \sqrt{3^{2}+4^{2}}=\sqrt{9 + 16}=\sqrt{25}=5 )

Step2: Calculate (\sin A), (\cos A), and (\tan A)

The definitions of trigonometric ratios are:

  • (\sin A=\frac{y}{r}), so (\sin A=\frac{4}{5})
  • (\cos A=\frac{x}{r}), so (\cos A=\frac{3}{5})
  • (\tan A=\frac{y}{x}), so (\tan A=\frac{4}{3})

Answer:

C. (\sin A=\frac{4}{5},\cos A=\frac{3}{5},\tan A=\frac{4}{3})