(tan²(<em>θ</em>) cos²(<em>θ</em>) - 1) / (1 + cos(2<em>θ</em>))
Recall that
tan(<em>θ</em>) = sin(<em>θ</em>) / cos(<em>θ</em>)
so cos²(<em>θ</em>) cancels with the cos²(<em>θ</em>) in the tan²(<em>θ</em>) term:
(sin²(<em>θ</em>) - 1) / (1 + cos(2<em>θ</em>))
Recall the double angle identity for cosine,
cos(2<em>θ</em>) = 2 cos²(<em>θ</em>) - 1
so the 1 in the denominator also vanishes:
(sin²(<em>θ</em>) - 1) / (2 cos²(<em>θ</em>))
Recall the Pythagorean identity,
cos²(<em>θ</em>) + sin²(<em>θ</em>) = 1
which means
sin²(<em>θ</em>) - 1 = -cos²(<em>θ</em>):
-cos²(<em>θ</em>) / (2 cos²(<em>θ</em>))
Cancel the cos²(<em>θ</em>) terms to end up with
(tan²(<em>θ</em>) cos²(<em>θ</em>) - 1) / (1 + cos(2<em>θ</em>)) = -1/2
Answer:
13,475
Step-by-step explanation:
First hour
350 people at $17.50 per ticket
350* $17.50 =$6125
Second hour
We add 20% more
350+350*.20 =350+70 =420
There were 420 people at $17.50
420*$17.50 =$7350
Add the total for the 2 hours
6125+7350=13,475
Answer:
6,5
Step-by-step explanation:
-2 is 4 down from 2, so reflected should be 4 up, or 6
Answer:
39
Step-by-step explanation:
Let x = number of child tickets sold.
Cost of x child tickets is x * 5.30 = 5.3x.
"three times as many adult tickets as child tickets were sold"
Number of adult tickets sold: 3x
Cost of 3x adult tickets is 3x * 8.40 = 25.2x
Cost of all tickets is 5.3x + 25.2x = 30.5x
Cost of all tickets is $1189.50
30.5x = 1189.5
x = 1189.5/30.5
x = 39
Answer: 39
Answer:
31.4 (simplified)
Step-by-step explanation:
C≈2π*5
C≈31.41593 (full answer)