<span>tan(15) =
sin(15) / cos(15) =
sin(45 - 30) / cos(45 - 30) =
[ sin(45)cos(30) - sin(30)cos(45) ] / [ cos(45)cos(30) + sin(45)sin(30)]
Since sin(45) = cos(45) = √2/2, you can just factor that out from the top and bottom
[ cos(30) - sin(30) ] / [ cos(30) + sin(30)]
[ √3/2 - 1/2 ] / [ √3/2 + 1/2]
(√3 - 1) / (√3 + 1)
(√3 - 1)^2 / (√3+1)(√3 - 1)
(√3 - 1)^2 / (3 - 1)
(3 - 2√3 +1) / 2
2 - √3
There's also a formula for tan(a-b), but I couldn't remember it off hand.</span>
40 ways. 6!/3!(6-3)! =120. We are only trying to find 3 ways. 120 is the total, 120/30 =40. So 40 is the answer.
Answer:
Step-by-step explanation:
The picture shows three isosceles tirangles with the same legs. The base of each triangle is 12 units, 5x-3 units and 17 units.
Since the angles at vertex of each isosceles triangles are 27°, 28° and 29°, then the lengths of the bases satisfy the double inequality
15<5x-3<17
Add 3 to this inequality
15+3<5x-3+3<17+3
18<5x<20
Divide it by 5:
Answer: a) reflected over x-axis and reflected over y-axis
<u>Step-by-step explanation:</u>
Reflection over the x-axis changes the sign of the y-coordinate
Z = (x, y) → Z'(x, -y)
Reflection over the y-axis changes the sign of the x-coordinate
Z' = (x, -y) → Z''(-x, -y)
A = (-4, 1) → A'' = (4, -1)
B = (-3, 2) → A'' = (3, -2)
C = (-1, 2) → A'' = (1, -2)
D = (-2, 1) → A'' = (2, -1)
