已知圆周角的余弦为4/5,求同弧所对的圆心角的正弦,余弦,正切

Question

已知圆周角的余弦为4/5,求同弧所对的圆心角的正弦,余弦,正切

Answer 1

设圆周角为θ度,则cosθ=4/5,0°﹤θ﹤90°,sinθ﹥0；
sinθ=√(1-cos²θ)=√[1-(4/5)²]=3/5
同弧所对的圆心角为2θ度；
sin2θ=2sinθcosθ
=2×3/5×4/5
=24/25
cos2θ=2cos²θ-1
=2×(4/5)²-1
=2×16/25-1
=32/25-1
=7/25
tan2θ=sin2θ/cos2θ
=(24/25)/(7/25)
=24/25×25/7
=24/7