What is the exact value of sin(345º)?

Step-by-step explanation:

Assuming we're in degrees, we have

sin(345) = sin(300 + 45)and using sin(A + B) = sinAcosB + sinBcosA, we have

sin300cos45 + sin45cos300 =

(-√3/2)(1/√2) + (1/√2)(1/2) =

-√3/ (2√2) + 1/(2√2) =

[ 1 - √3 ] / (2√2) and rationalizing the denominator, we have

√2 [ 1 - √3] / 4 =

(√2 - √6) / 4

I hope it's helpful!!

geometric series converge the common ratio r has magnitude less than one.

which is equivalent to

for the example we need

|2-x| < 1

-1 < 2-x   and 2-x < 1

x < 3 and x > 1

we can write that

answer: 1 < x < 3

1a. common ratio r=250/25=10 > 1     diverges

1b.   r=50/100=1/2 converges

when these converge they converge to

where a is the first term.

answer: 200

1c. r=-1   so it's not the case that |r| < 1.     diverges

2a. x is the common ratio so we converge when |x|< 1

2b.   r=-10x / -2 = 5x.

we converge when

|5x| < 1

|x| < 1/5

2c.   r=3-2x

-1 < 3-2x and 3-2x < 1

-4 < -2x and 2 < 2x

x < 2 and 1 < x

1 < x < 2

2d. [/tex] r=-48x^3/12 = 4x^3[/tex]

|4x^3| < 1

|x^3| < \frac 1 4

|x| < 4^{-1/3}