Question

question 6 (1 point)
the point (-3,4) is on the terminal arm of ∠a.which is the correct value of sec a?
◯ a) 5/4
◯ b) -3/5
◯ c) 4/5
◯ d) -5/3

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: Recall the definition of secant

The definition of \( \sec A=\frac{r}{x} \). Substitute \( r = 5,x=-3 \) into the formula, we get \( \sec A=\frac{5}{-3}=-\frac{5}{3} \).

Answer:

d) \(-\frac{5}{3}\)