Question

The line with equation -a+3b=0 coincides with the terminal side of an angle θ in standard position and sin θ<0. What is the value of cosθ?

Option 1: 1/3
Option 2: √10
Option 3: -√10/10
Option 4: -3√10/10

Answer 1

The value of cos(theta) is 1/3.

Step-by-step explanation:

To find the value of cos(theta) when sin(theta)<0 and the line -a+3b=0 coincides with the terminal side of angle theta, we can use the equation sin^2(theta) + cos^2(theta) = 1. Since sin(theta)<0, we know that cos^2(theta) must be less than 1, so cos(theta) must be less than 1. Therefore, the correct answer is Option 1: 1/3.