Answer:
x = 1 in
Step-by-step explanation:
We can use ratios to solve since they are similar triangles
6 6+x
----- = ---------
5 6
Using cross products
6*6 = 5*(6+x)
36 = 30+6x
Subtract 30 from each side
36-30 = 30-30+6x
6 = 6x
Divide each side by 6
6/6 = 6x/6
1 =x
125 = 5 * 5 * 5 = 5^3
Its a perfect cube.
Rewrite this symbolically: 6(2/6) = 12/6 = 2 (answer)
An equally good approach would be to cancel the 6's, obtaining 2 (answer)
I'll write "x" instead theta.
sin x + 1 = cos(2x)
formula: cos(2x) = 1 - 2sin²x
sin x + 1 = 1 - 2sin²x
2sin²x + sin x = 0
sin x (2sin x + 1) = 0
sin x = 0 or sin x = -1/2
x1 = πk and x2 = -π/6 + 2πk and
x3 = 5π/6 + 2πk
for domain 0≤x<2π :
x1 = 0 (for k=0 in x1)
x2 = π (for k=1 in x1
x3 = 11π/6 (for k=1 in x2)
x4 = 5π/6 (for k=0 in x3).
k is an integral.
