作业帮求三角函数方程求α,142rad,0.785rad
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求三角函数方程求α,142rad,0.785rad
求三角函数方程
求α,142rad,0.785rad
求三角函数方程求α,142rad,0.785rad
2tan α+4=3√2sec α,
2sin α/cos α+4=3√2/cos α,
2sin α+4cos α=3√2,得sin α=（3√2-4cos α）/2,代入
(sin α)^2+(cos α)^2=1,得cos α=7√2/10或cos α=√2/2.
所以α=arccos(7√2/10)≈8.13度=8.13÷180×3.14≈0.142rad或
α=arccos(√2/2)=45度=45÷180×3.14=0.785rad.
2tanα+4=3√2secα
2sinα/cosα+4=3√2/cosα
2sinα+4cosα=3√2
(sinα)^2+(cosα)^2=1
所以cosα=7√2/10或√2/2