if cos(theta)>0, then in which quadrants would theta lie?

1 Answer

  • TomV
    Lv 7
    1 month ago

    Since the cosine is the projection of the terminal line onto the x-axis, and we assume  a "standard" x-y axis configuration, positive x to the right of the y axis, the projection would be positive when the terminal line lies to the right of the y-axis.

    So you should be able to visualize the positive values of cosΘ on the +x axis which would put Θ in the 1st and 4th quadrants.

    Similarly, cosΘ < 0 would put the terminal line to the left of the y-axis in quadrants 2 and 3.

    A similar visualization of the sine being the projection on the y-axis where the values are positive above the x-axis in quadrants 1 and 2, with negative values below the x-axis in quadrants 3 and 4.

    In summary, the cosine is positive in quadrants 1 and 4, and the sine is positive in quadrants 1 and 2.

Still have questions? Get answers by asking now.