what are the x and y components of a 25m displacement at an angle of 210degree with the x-axis anti clockwise
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y = -12.5
x = -21.66 (Approx.)
210° in the anticlockwise direction means 30° below the negative x-axis.
Now, from the end of 25m line make a Horizontal and Vertical line till they touch the axes. We'll see a right-angled triangle now.
Applying Trigonometric Ratios
By applying Sine of 30°, we'll find the y-component and by applying Cosine of 30°, we'll find the x-component.
Therefore,
sin(30°) = y/25
or, 1/2 = y/25
or, 1 = 2y/25
or, 2y = 25
or, y = 25/2
or, y = -12.5 (Negative sign will be there as we are taking negative y-axis here)
Now,
cos(30°) = x/25
or, √3/2 = x/25
or, x = √3*25/2
or, x = -21.66(approx.)(Negative sign will be there as we are taking negative x-axis here)
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