若cos(-820)=t,则tan（-440)的值为

Question

若cos(-820)=t,则tan（-440)的值为

Answer 1

cos(-820°) = cos(-720°-100°) = cos(-100°) = cos100°= t < 0
tan(-440°)
= tan(-360°- 80°)
= tan( -80°)
= tan(180°-80°)
= tan100°
因为：(sec100°)^2 = 1/(cos100°)^2 = 1/t^2 = 1 + (tan100°)^2
(tan100°)^2 = 1/t^2 - 1 = (1-t^2)/t^2
所以，
tan100°= - √(1-t^2) /|t| = √(1-t^2) /t