By definition of tangent,
tan(2<em>θ</em>) = sin(2<em>θ</em>) / cos(2<em>θ</em>)
Recall the double angle identities:
sin(2<em>θ</em>) = 2 sin(<em>θ</em>) cos(<em>θ</em>)
cos(2<em>θ</em>) = cos²(<em>θ</em>) - sin²(<em>θ</em>) = 2 cos²(<em>θ</em>) - 1
where the latter equality follows from the Pythagorean identity, cos²(<em>θ</em>) + sin²(<em>θ</em>) = 1. From this identity we can solve for the unknown value of sin(<em>θ</em>):
sin(<em>θ</em>) = ± √(1 - cos²(<em>θ</em>))
and the sign of sin(<em>θ</em>) is determined by the quadrant in which the angle terminates.
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We're given that <em>θ</em> belongs to the third quadrant, for which both sin(<em>θ</em>) and cos(<em>θ</em>) are negative. So if cos(<em>θ</em>) = -4/5, we get
sin(<em>θ</em>) = - √(1 - (-4/5)²) = -3/5
Then
tan(2<em>θ</em>) = sin(2<em>θ</em>) / cos(2<em>θ</em>)
tan(2<em>θ</em>) = (2 sin(<em>θ</em>) cos(<em>θ</em>)) / (2 cos²(<em>θ</em>) - 1)
tan(2<em>θ</em>) = (2 (-3/5) (-4/5)) / (2 (-4/5)² - 1)
tan(2<em>θ</em>) = 24/7
Answer:
C $113.40
Step-by-step explanation:
100%-40%=60%
$180x60/100
=$10800/100
=$108
100%+5%(tax)=105%
$108x105/100
=$11340/100
=$113.40 (C)
Answer:
2x + 4y =8
substitute 0 for x
2 (0) + 4y = 8
0 +4y = 8
subtract 0 from both sides
-0 +4y =8 - 0
4y = 8
Divide both sides by 4
Y = 2
Step-by-step explanation:
<h3>
Answer: 0.05x+10</h3>
Work Shown:
x = number of miles
Cost of company A = 0.09x+50.50
Cost of company B = 0.14x+60.50
Subtract the two expressions (B-A) to find the difference in price
B-A = (0.14x+60.50)-(0.09x+50.50)
B-A = 0.14x+60.50-0.09x-50.50
B-A = (0.14x-0.09x) + (60.50-50.50)
B-A = 0.05x+10
Answer:
6 pounds
Step-by-step explanation:
