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.
<em />
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:
Slope is going to be the "M" or gradient of the line. It represents the change in the Y value over time as the line continues. It tells you how high or low it points depending on what the slope is.
Thanks for letting me help!!
Answer:
The fifth term is 620
Step-by-step explanation:
y=40×(-2)^(n-1)
The 5th terms means n=5
y = 40 * (-2) ^ (5-1)
= 40 * (-2) ^4
= 40 * (16)
= 640
34 = -2t....divide both sides by -2
(-34/2) = (-2/-2)t
- 17 = 1t, or just t
so ur answer is : t = -17
Answer:
84% or 21/25
Step-by-step explanation:
1 is 8, 2 is 6, 3 is 9, 4 is 11, 5 is 9, 6 is 7. add the values: We get 50.
because landing on 1 is an 8/50 chance, not landing on one is a 42/50 chance, which in turn is 84% or 21/25.
