sica asked in Science & MathematicsMathematics · 1 month ago

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

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• 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.

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