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slava [35]
3 years ago
12

Arrange the steps in the correct order to express cos3x in terms of cosx cos(2x)cos(x)-sin(2x)(x) [1-sin^2(x)]cos(x)-[2sin(x)cos

(x)]sin(x) cos(x)-4sin^2(x)cos(x) 4cos^3(x)-3cos(x) cos(2x+x) cos(x){1-4[1-cos^2(x)]} cos(x)-2sin^2(x)cos(x)-sin^2(x)cos(x) cos(x)[1-4sin^2(x)] cos(x)[-3+4cos^2(x)]
Mathematics
1 answer:
noname [10]3 years ago
4 0

cos(3x) = cos(2x+x)

= cos(2x) cos (x) -sin(2x)sin(x)

=(1-2sin^2(x)) cos(x)-(2 sin(x) cos(x)) sin(x)

= cos x -2sin^2(x) cos(x) -2sin^2(x) cos(x)

= cos(x) - 4 sin^2(x) cos(x)

cos(x)(1-4sin^2(x))

=cos(x(1-4(1-cos^2(x))

=cos(x)(1-4+4cos^2(x))

= cos(x)-4cos(x)+4cos^3(x)

=-3cos(x)+4cos^3(x)

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Find the formula for the nth term of the arithmetic sequence -39, 61, 161, 261, ...
maksim [4K]
<h3>Given that it is arithmetic</h3>

d = a_{2} - a_{1} = 61 - ( - 39) = 100

a_{n} = a_{1} + (n - 1)d \\ a_{n} = - 39+ 100 (n - 1) \\ a_{n} =  - 39 + 100n - 100 \\ a_{n} =  - 139 + 100n

6 0
1 year ago
ASAP please help!!!
Serggg [28]
Y+4<u><</u>9
subtract 4
y<u><</u>5
y is smaller than and equal to 5
so you shade from 5 to the negative end to infinity (to the left) and shade the 5 to show that it is included (attachment says A)







6 less than (-6) 2 times a number (2 time x) is greater than (>) 8 (8)

-6+2x>8
add 6
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divide 2
x>7
so
x is bigger than 7
shade from 7 to the positive end to infinity (to the right) and don't shade 7 but put a circle around it to show that it is not included (attachment says B )

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4 0
3 years ago
1. Find the phase shift of the function y = 5cos(2x + pi/2).
kolezko [41]

Answer:

see explanation

Step-by-step explanation:

1

The cosine function in standard form is

y = acos(bx + c)

where a is the amplitude, period = \frac{2\pi }{b} and

phase shift = - \frac{c}{b}

here b = 2 and c = \frac{\pi }{2}, thus

phase shift = - \frac{\frac{\pi }{2} }{2} = - \frac{\pi }{4}

2

the amplitude = | a |

which has a maximum of a and a minimum of - a

y = 4cosx ← has a maximum value of 4

5 0
3 years ago
Tim wants to determine the height, x, of a nearby tree. He stands 35 feet
kodGreya [7K]

Answer:

x ≈ 29.4 ft

Step-by-step explanation:

The model is a right triangle.

Using the tangent ratio

tan40° = \frac{opposite}{adjacent} = \frac{x}{35} ( multiply both sides by 35 )

35 × tan40° = x , then

x ≈ 29.4 ft ( to 1 dec. place )

6 0
2 years ago
What is the value of h in the figure below?
yaroslaw [1]

Answer:

12

Step-by-step explanation:

ΔBAD is similar to ΔCBD.  So we can write a proportion:

BD / CD = AD / BD

h / 16 = 9 / h

h² = 144

h = 12

5 0
3 years ago
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