Suppose theta is an angle in standard position with cos theta > 0. In which quadrants could the terminal side of theta lie? Select two answers.
I
II
III
IV
I don't know what this means:(
Connections Academy Precalculus B Unit 1 Lesson 6
B
B
B
AD
B
(its a lot of B i know)
Nvm the answer is I and IV
Quadrants I and IV?
100% thanks boo
thanks
Boo is write as of 2/10/2023 ;)
Draw a triangle in standard position. That is, with one corner at (0,0) and one side along the x-axis. The 3rd point is in one of the quadrants.
cosθ = x/r
so, in which quadrants is x positive?
Did you find the right answer
right*
No worries! Let's break it down.
In the coordinate plane, the standard position refers to an angle whose vertex is at the origin (0,0) and whose initial side lies along the positive x-axis. The terminal side of the angle is the side that moves away from the origin.
When it's mentioned that "cos theta > 0," it means that the cosine of angle theta is positive. In the unit circle, cos theta represents the x-coordinate of the point where the terminal side of theta intersects the unit circle.
Now, let's determine the possible quadrants where the terminal side of theta could lie.
In Quadrant I, both the x and y-coordinates are positive.
In Quadrant II, the x-coordinate is negative, but the y-coordinate is positive.
In Quadrant III, both the x and y-coordinates are negative.
In Quadrant IV, the x-coordinate is positive, but the y-coordinate is negative.
Since cos theta is positive, it means that the x-coordinate of the point on the unit circle is positive.
Considering this information, we can conclude that the terminal side of theta could lie in Quadrant I or Quadrant IV, as these are the only quadrants where the x-coordinate is positive.
Therefore, the possible answers are:
I
IV