+24 Let cos(−θ) = 4 / 5 and tanθ > 0.
What is the value of sin(−θ)?
4 / 3
−4 / 5
4 / 5
−3 / 5
+9481 By the Pythagorean identity...
( sin(-θ) )2 + ( cos(-θ) )2 = 1
We are given that cos(-θ) = 4/5
( sin(-θ) )2 + ( 4/5 )2 = 1
( sin(-θ) )2 + 16/25 = 1
Subtract 16/25 from both sides of the equation.
( sin(-θ) )2 = 1 - 16/25
( sin(-θ) )2 = 9/25
Take the ± square root of both sides.
sin(-θ) = ±√[ 9/25 ]
sin(-θ) = ± 3 / 5
Since cos(-θ) is positive, -θ must be in Quadrant I or Quadrant IV.
Since tan θ > 0 , θ must be in Quadrant I or III. That means -θ must be in Quadrant IV or II .
So -θ has to be in Quadrant IV, and sin(-θ) has to be negative.
sin(-θ) = - 3 / 5
