Question

multiple choice 11 points
(-3,4) is a point on the terminal side of an angle in standard position. what is the value of cosθ?
-3/5
-4/5
3/4
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 \(x = - 3\), \(y = 4\), so \(r=\sqrt{(-3)^{2}+4^{2}}=\sqrt{9 + 16}=\sqrt{25}=5\).

Step2: Use the cosine formula

The formula for \(\cos\theta=\frac{x}{r}\). Substituting \(x=-3\) and \(r = 5\), we get \(\cos\theta=\frac{-3}{5}\).

Answer:

\(\frac{-3}{5}\) (corresponding to the first option \(\frac{-3}{5}\))