Question

question 26 (1 point) page 26 of 35 the point (3, -5) is on the terminal arm of dd. 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 = -3 / √34, cos d = 5 / √34, tan d = -5 / 3 c) sin d = -5 / √34, cos d = 3 / √34, tan d = -5 / 3 d) sin d = -√34 / 5, cos d = √34 / 3, tan d = -3 / 5

Explanation:

Step1: Calculate the radius \( r \)

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

$$ r=\sqrt{3^{2}+(-5)^{2}}=\sqrt{9 + 25}=\sqrt{34} $$

Step2: Find the sine ratio

The formula for sine is \( \sin D=\frac{y}{r} \). Here \( y=-5 \) and \( r = \sqrt{34} \), so \( \sin D=\frac{-5}{\sqrt{34}} \).

Step3: Find the cosine ratio

The formula for cosine is \( \cos D=\frac{x}{r} \). Here \( x = 3 \) and \( r=\sqrt{34} \), so \( \cos D=\frac{3}{\sqrt{34}} \).

Step4: Find the tangent ratio

The formula for tangent is \( \tan D=\frac{y}{x} \). Here \( y=-5 \) and \( x = 3 \), so \( \tan D=\frac{-5}{3} \).

Answer:

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