Friction force F and sin α cos α Reference relation of equal trigonometric function That is, when to use sin when the inclination angle on the inclined plane has F α Or cos α For example, what does f = mgcosa mean, and what is the difference between uphill and downhill angles?

Set the inclination of the inclined plane as θ, So the sliding component of gravity is mgsin θ, The pressure of an object on an inclined plane is mgcos θ, Then, when the object goes up along the inclined plane, let the friction coefficient be μ, Then the resultant force F = mgsin θ+μ mgcos θ； When the object is inclined downward, the resultant force F = mgsin θ-μ mgcos θ. This is limited to the scope of Statics (this means that when an object moves on an inclined plane, the inclined plane has no displacement relative to the ground.)
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What is the relationship between trigonometric function sin and cos?

sinx=cos(90-x)
Sin squared + cos squared equals 1

Trigonometric function proof: (COS) α－ 1） ²+ sin ²α= 2－2cos α?

Left = (COS) α－ 1） ²+ sin ²α
=cos ²α- 2cos α+ 1+sin ²α
=(sin ²+ cos ²α)- 2cos α+ one
=1-2cos α+ one
=2－2cos α= right
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If the train moves in a straight line with uniform acceleration from standstill and travels 540M within 1min, its displacement in the first 10s is () A. 90m B. 45m C. 30m D. 15m

x=1
2at2, a = 2x
T2 = 0.3m/s2, so the displacement X '= 1 in the first 10s
2at2 = 15m. Therefore, D is correct and a, B and C are wrong
Therefore, D

Someone estimated the acceleration of the train with a watch. He observed it for 3 minutes and found that the train was moving 540M; After an interval of 3 min, the train was observed for 1 min, and it was found that the train was moving 360 M Suppose the train moves in a straight line with uniform acceleration, what is the estimated acceleration of the train? [hope to have a complete process, with formula]

The average speed in the first three minutes is 180m / min, and the speed in the next four minutes is 90m / min. since the average speed is the speed in the middle of the time period, the interval between the two average speeds is 3.5min, and a = 180 / 7 m / min is obtained from at = v0-v1 ²

A train starts to move in a straight line with uniform acceleration from standstill and runs 540M in the first 1min. What is its displacement in the first 10s?

From the solution of formula: x = at ^ 2 / 2: 540 = at ^ 2 / 2: a = 0.3m/s ^ 2
When T1 = 10s, X1 = AT1 ^ 2 / 2 = 0.3 × 100/2=15m

Friction force F and sin α cos α Reference relation of equal trigonometric function That is, when to use sin when the inclination angle on the inclined plane has F α Or cos α For example, what does f = mgcosa mean, and what is the difference between uphill and downhill angles?