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Luba_88 [7]
3 years ago
13

Prove that sin20sin40sin60sin80=3/16

Mathematics
1 answer:
never [62]3 years ago
5 0
We'll use the following properties of sine and cosine to prove this:

sin(a)\cdot sin(b) = \frac12(cos(a-b) - cos(a+b))

cos(a)\cdot cos(b) = \frac12(cos(a+b) + cos(a-b))

cos(180+a) = cos(180-a)

Then it's just a matter of filling it in...

sin20sin40 * sin60sin80 = 1/2(cos20 - cos60) * 1/2 (cos20 - cos140) =

1/8( cos40 + 1 - cos160 - cos120 - cos40 - cos80 + cos80 + cos200) =

1/8(1 -  cos160 - cos120 + cos200) =

1/8(1 -  cos160 - cos120 + cos160) =

1/8(1 - cos120 ) = 1/8( 1 + 1/2 ) = 3/16

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What is the value of the natural logarithm when x =0.6 is rounded to the nearest hundredth
Bezzdna [24]
We are tasked to determine the natural logarithm when x = 0.6. 
x = 0.6, applying natural logarithm on both sides, we have it:
ln x = ln 0.6 using a scientific calculator, enter ln 0.6 and then this would give an answer of -0.5108256238
As per instruction, we are required to round the answer to the nearest hundredth such as the final answer is -0.51.

The answer is the letter "B".
3 0
3 years ago
Read 2 more answers
Given that (6,-8) is on the graph for f(x), find the corresponding point for the function f(x+1)
Sever21 [200]

Answer: ( 5, -8)

Step-by-step explanation:

3 0
3 years ago
Please help me now ! Thank you
jarptica [38.1K]
First we'll do two basic steps. Step 1 is to subtract 18 from both sides. After that, divide both sides by 2 to get x^2 all by itself. Let's do those two steps now

2x^2+18 = 10
2x^2+18-18 = 10-18 <<--- step 1
2x^2 = -8
(2x^2)/2 = -8/2 <<--- step 2
x^2 = -4

At this point, it should be fairly clear there are no solutions. How can we tell? By remembering that x^2 is never negative as long as x is real. 

Using the rule that negative times negative is a positive value, it is impossible to square a real numbered value and get a negative result. 

For example
2^2 = 2*2 = 4
8^2 = 8*8 = 64
(-10)^2 = (-10)*(-10) = 100
(-14)^2 = (-14)*(-14) = 196

No matter what value we pick, the result is positive. The only exception is that 0^2 = 0 is neither positive nor negative.

So x^2 = -4 has no real solutions. Taking the square root of both sides leads to

x^2 = -4
sqrt(x^2) = sqrt(-4)
|x| = sqrt(4)*sqrt(-1)
|x| = 2*i
x = 2i or x = -2i
which are complex non-real values


5 0
3 years ago
Use the box method to distribute and simplify (3x – 1)(-5x + 1)
Softa [21]

Answer:

-15x^2 +8x -1

Step-by-step explanation:

(3x – 1)(-5x + 1)=

3x(-5x) + 3x(1) - 1(-5x) -1 =

-15x^2 +3x +5x -1 =

-15x^2 +8x -1

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hope it helps.

4 0
3 years ago
What is the distance between (2,-9) and (-1,4)
kkurt [141]

Answer:

total distance might be 16

Step-by-step explanation:

|y2-y1/x2-x1|, plug it the numbers, if you got a negative number, its just positive since the equation is set to absolute value

7 0
2 years ago
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