Answer:
sin(2Θ) = -0.199
cos(2Θ) = 0.98
tan(2Θ) = -0.203
Step-by-step explanation:
sin(Θ) = -0.1
therefore Θ = -5.74° because Θ is in the fourth quadrant.
cos(Θ) = [tex]\sqrt{1 - sin^2\theta} = \sqrt{1 - (0.1)^2} = \sqrt{0.99} = 0.995[/tex]
i) sin(2Θ) = 2sin(Θ)cos(Θ) = 2 [tex]\times[/tex] (-0.1) [tex]\times[/tex] 0.995 = -0.199
ii) cos(2Θ) = [tex]cos^{2} \theta - sin^{2} \theta = (0.995)^{2} - (-0.1)^{2} = 0.99 -0.01 = 0.98[/tex]
iii) tan(2Θ) = [tex]\frac{-0.199}{0.98} = -0.203[/tex]
