A golfer takes two putts to sink the ball, one is (81.6 ft, 31.7 degrees N of E) and the other is (3.20 ft, 53.4 degrees W of N). What is the displacement of the single putt that would sink the ball on the first try?
Well, what I did was make a diagram of the two vectors,
I named the first one Alpha and tried to find both of their components.
Alpha-subX (for the x component)
Alpha-subX = 81.6 ft * cos(31.7) = 69.426
Alpha-subY (for the y component)
Alpha-subY = 81.6 ft * sin(31.7) = 42.878
I also did the same thing for the 2nd putt, and named it Beta.
Beta-subX = 3.20 ft cos(53.4) = 1.907
Beta-subY = 3.20 ft sin(53.4) = 2.569
I "think" I'm supposed to combine the x components with each other
Alpha subX + Beta subX
and Alpha subY + Beta subY
Yes, exactly BUT THE SECOND ONE was west of north
x distance = 69.4 -3.2 sin 53.4 = x
y distance = 42.9 + 3.2 cos 53.4 = y
d = sqrt (x^2 + y^2)
tan of angle north of east = y/x
What do you mean, I did indicate on the question that it was west of north?
But going west is NEGATIVE x
Why did you swap Betas trig functions?
This is right:
Alpha-subX (for the x component)
Alpha-subX = 81.6 ft * cos(31.7) = 69.426
Alpha-subY (for the y component)
Alpha-subY = 81.6 ft * sin(31.7) = 42.878
This is WRONG
Beta-subX = 3.20 ft cos(53.4) = 1.907
Beta-subY = 3.20 ft sin(53.4) = 2.569
I CLAIM
Beta-subX = -3.20 ft SIN(53.4) = 1.907
Beta-subY = 3.20 ft COS(53.4) = 2.569
Draw a picture
Because the angle 53.4 is left from the Y axis, not up from the X axis.
They tricked you with the west of north
that is left of the Y axis
DRAW the picture.
How do I know which trig function to use?
I made my second triangle like this
_____
\ |
\ |
\ |
\|
Wait that's not how it's supposed to look.
Ok
copied your result, should be
I CLAIM
Beta-subX = -3.20 ft SIN(53.4) = -2.56
Beta-subY = 3.20 ft COS(53.4) = 1.90
when the angle is in quadrant II
53.4 degrees left of north
then east component is - sin
then north component is + cos
if you want the angle from the x axis then it is
90 - 53.4 = 36.6
then you could use cos and sin like you want because
sin (90-x) = cos x
cos (90-x) = sin x :)