Question

the point (3, -5) is on the terminal arm of ∠d. which is the set of exact primary trigonometric ratios for the angle?
a) sin d = -5/√34, cos d = -3/√34, tan d = 5/3
b) sin d = -5/√34, cos d = 3/√34, tan d = -5/3
c) sin d = 5/√34, cos d = -3/√34, tan d = -5/3
d) sin d = 3/√34, cos d = -5/√34, tan d = -3/5

Explanation:

Step1: Calculate the radius \( r \)

For a point \((x,y)\) on the terminal side of an angle, \(r=\sqrt{x^{2}+y^{2}}\). Here \(x = 3\) and \(y=-5\), so \(r=\sqrt{3^{2}+(-5)^{2}}=\sqrt{9 + 25}=\sqrt{34}\).

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

The formulas for trigonometric ratios are \(\sin D=\frac{y}{r}\), \(\cos D=\frac{x}{r}\) and \(\tan D=\frac{y}{x}\).
Substituting \(x = 3\), \(y=-5\) and \(r=\sqrt{34}\):
\(\sin D=\frac{-5}{\sqrt{34}}\), \(\cos D=\frac{3}{\sqrt{34}}\), \(\tan D=\frac{-5}{3}\).

Answer:

B. \(\sin D=-\frac{5}{\sqrt{34}}\), \(\cos D=\frac{3}{\sqrt{34}}\), \(\tan D=-\frac{5}{3}\)