Question

question 6 (1 point)
the point (3, 4) is on the terminal arm of da.which is the set of exact primary trigonometric ratios for the angle?

a) \\( \sin a=\frac{4}{5}, \cos a=\frac{3}{5}, \tan a=\frac{3}{4} \\)

b) \\( \sin a=\frac{4}{5}, \cos a=\frac{3}{5}, \tan a=\frac{4}{3} \\)

c) \\( \sin a=\frac{3}{5}, \cos a=\frac{4}{5}, \tan a=\frac{4}{3} \\)

d) \\( \sin a=\frac{5}{4}, \cos a=\frac{5}{3}, \tan a=\frac{3}{4} \\)

Explanation:

Step1: Calculate the radius \( r \)

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

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

The formulas are \(\sin A=\frac{y}{r}\), \(\cos A=\frac{x}{r}\), \(\tan A=\frac{y}{x}\).
Substituting \(x = 3,y = 4,r = 5\) into the formulas:

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

Answer:

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