The changes in the force components(f_x and f_y) as the angle θ increases from 0° to 90° is that;
The horizontal force component f_x decreases from 60 N to 0 N while the vertical force component f_y increases from 0 N to 60 N.
We are told the man exerts a force of 60N at an angle of θ. If we resolve the force into the horizontal(x - component) and vertical(y - component), we have;
Horizontal Component; f_x = 60cosθ
Vertical Component; f_y = 60sinθ
We want to find f_x and f_y when θ = 0°,45°, and 90°.
Thus;
When θ = 0;
cos 0° = 1 and sin 0° = 0
∴ f_x = 60 × 1
f_x = 60 N
f_y = 60 × 0
f_y = 0 N
When θ = 45°;
cos 45° = 0.7071 and sin 45° = 0.7071
Thus;
f_x = 60 × 0.7071
f_x = 42.43 N
f_y = 60 × 0.7071
f_y = 42.43 N
When θ = 90°;
cos 90° = 0 and sin 90° = 1
∴ f_x = 60 × 0
f_x = 0 N
f_y = 60 × 1
f_y = 60 N
From the above calculations, we can see that as θ increases from 0° to 90°, the horizontal force component f_x decreases from 60 N to 0 N while the vertical force component f_y increases from 0 N to 60 N.
Lastly, the graph of sin θ and cos θ has been attached showing how their values increase or decrease as angle increases from 0 to 90°.
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