From the figure, we immediately have
cos(θ) = 8/17
sin(θ) = 15/17
By definition of tangent,
tan(2θ) = sin(2θ)/cos(2θ)
Recall the double angle identities:
sin(2θ) = 2 sin(θ) cos(θ)
cos(2θ) = cos²(θ) - sin²(θ) = 2 cos²(θ) - 1
Then
tan(2θ) = (2 sin(θ) cos(θ)) / (2 cos²(θ) - 1)
tan(2θ) = (2 × 15/17 × 8/17) / (2 × (8/17)² - 1)
tan(2θ) = -240/161
To write 23/8 as a decimal you have to divide numerator by the denominator of the fraction.
<span>We divide now 23 by 8 what we write down as 23/8 and we get 2.875 </span>
<span>And finally we have: </span>
23/8 as a decimal<span> equals </span><span>2.875</span>
Subtraction:
2115 (20:15) - 0830 (8:30) = 20:75 - 8:30 = 12:45 P.m. = 1245
Hope it helped,
Happy homework/ study/ exam!
