sec[arcsin(3127/3145)],怎么求值
求(3127/3145)的反正弦,再正割值
sec[arcsin(3127/3145)]
=1/cos[arcsin(3127/3145)]
≈1/cos83.867°
≈1/0.10683675
≈9.36
设:arcsin(3127/3145)=α
∴sinα=3127/3145
cosα
=√﹙1-sin²α﹚
=√[1-﹙3127/3145﹚²]
=√[﹙3145²-3127²﹚/3145²]
=√[﹙3145+3127﹚×﹙3145-3127﹚/3145²]
=√[﹙6272×18﹚/3145²]
=√[﹙2^5×14²﹚×﹙2×3²﹚/3145²]
=√[﹙2^6×14²×3²﹚/3145²]
=√﹙2³×14×3﹚²/3145²]
=√336²/3145²
=336/3145
secα
=1/cosα
=1/﹙336/3145﹚
=3145/336
≈9.36
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