The angle θ is in the second quadrant and tan θ = -3/5. Point P is on the terminal arm of angle θ/ Which is a possible coordinate for P?
A) (-5,√29)
B) (-3,√29)
C) (-10,6)
D) (-6,10)
I drew the triangle, and aren't the coordinates supposed to be (-5,-3)? However the answer is C, I don't get it, can someone please explain?
tanØ = y/x
since tanØ = -3/5 and you are in II
then y = 3, and x = -5 , or in that ratio
now look at C) with point (-10,6)
isn't tanØ = 6/-10 = -3/5 ??
It said "possible point", other points could have been
(-20,12), (-200, 120) etc
(in your diagram, the end point in II should have been (-5,3) , not (-5,-3) )
To solve this problem, we can use the trigonometric ratios and the properties of angles in the second quadrant.
Given that tan θ = -3/5, we can determine the values of the adjacent and opposite sides of the triangle formed in the second quadrant.
Let's label the triangle as follows:
Adjacent side: -3
Opposite side: 5
Using the Pythagorean theorem, we can find the hypotenuse of the triangle:
Hypotenuse = √((-3)^2 + 5^2) = √(9 + 25) = √34
Now, let's consider the negative signs for the coordinates in the second quadrant. In the second quadrant, the x-coordinate is negative, and the y-coordinate is positive.
Therefore, the possible coordinate for point P would be (-3, √34), which is not listed as an option.
However, it seems like there might be an error in the given answer choices. Let's check each of them:
A) (-5, √29): This coordinate does not match the values we calculated for the triangle, so it is not correct.
B) (-3, √29): This coordinate does not match the values we calculated for the triangle, so it is not correct.
C) (-10, 6): This coordinate does not match the values we calculated for the triangle, so it is not correct.
D) (-6, 10): This coordinate does not match the values we calculated for the triangle, so it is not correct.
Based on our calculations, it appears that none of the given answer choices match the correct coordinate based on the given conditions. There might be an error in the answer options or in the given information.