question 26 (1 point) page 26 of 35 the point (3, -5) is on the terminal arm of dd. which is the set of…

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
Answer
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} )