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
You just find the quartiles which are 62 and 50 the mines them which equals 12.
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Answer:
1680 possible pizzas
Step-by-step explanation:
Pizza contains 2 different meat and 3 different vegetables.
If there are 5 meats and 8 vegetables, the customer can select any one of 3 types of crust.
Total number of ways to select meat = 5C2
nCr = n! /(n-r)! r!
5C2 = 5! / (5-2)!2!
= 5! / 3!2!
= 10
Total number of ways to select vegetables = 8C3
= 8!/(8-3)!3!
= 8! / 5!3!
= 56
Total number of pizza choice that can be made = 3 * 5C2 * 8C3
= 3*10*56
= 1680 possible pizza
Answer:
<h2>x = 2</h2>
Step-by-step explanation:
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The steps of the solution in the photo above
I hope that is useful for you :)
