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4 years ago

(Photo attached) Trig question. Thanks in advance! :)

Mathematics

1 answer:

kolbaska11 [484]4 years ago

4 0

Answer:

a) cos(α+β) ≈ 0.8784

b) sin(β -α) ≈ -0.2724

Step-by-step explanation:

There are a couple of ways to go at these. One is to use the sum and difference formulas for the cosine and sine functions. To do that, you need to find the sine for the angle whose cosine is given, and vice versa.

Another approach is to use the inverse trig functions to find the angles α and β, then combine those angles and find find the desired function of the combination.

For the first problem, we'll do it the first way:

sin(α) = √(1 -cos²(α)) = √(1 -.926²) = √0.142524 ≈ 0.377524

cos(β) = √(1 -sin²(β)) = √(1 -.111²) ≈ 0.993820

a) cos(α+β) = cos(α)cos(β) -sin(α)sin(β)

= 0.926×0.993820 -0.377524×0.111

cos(α+β) ≈ 0.8784

b) sin(β -α) = sin(arcsin(0.111) -arccos(0.926)) ≈ sin(6.3730° -22.1804°)

= sin(-15.8074°)

sin(β -α) ≈ -0.2724

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zubka84 [21]

Answer:

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: D

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3. Counterclockwise rotation by π/2 radians

: F

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5. Reflection about the y-axis : A

6. Reflection about the line y = x : B

Step-by-step explanation:

Given a linear transformation $T:\mathbb{R}^2\to\mathbb{R}^2$ , one matrix representation of T is obtained by stacking the vectors T(1,0) and T(0,1) in columns.

a) A counter clockwise rotation of $\pi/2$ radians sends (1,0) to (0,-1) and it sends (0,1) to (1,0), so the matrix representation is

$\left[\begin{matrix} 0& 1 \\ -1 & 0 \end{matrix}\right]$ which corresponds to matrix D.

From now on, I will provide the values of T(1,0) and T(0,1)

b) Reflection about the x-axis T(1,0) = (1,0) and T(0,1) = (0,-1), which corresponds to matrix E.

c) Counterclockwise rotation by π/2 radians T(1,0) = (0,1), T(0,1) = (-1,0). Matrix F

d) The projection onto the x-axis given by T(x,y) = (x,0). T(1,0) = (1,0) T(0,1) = (0,0). Matrix C

e) Reflection about the y-axis T(1,0) = (-1,0) T(0,1) = (0,1). Matrix A

f) Reflection about the line y = x. This transformation corresponds to interchanging the values of x and y. That is, send (x,y) to (y,x). So, in this case

T(1,0) = (0,1) T(0,1) = (1,0). Matrix B

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3 years ago

Derivative of x^3 + 5y^2=2

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Answer:

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Step-by-step explanation:

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AlexFokin [52]

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3 years ago

Read 2 more answers

MARKING BRAINLIEST!!!<br><br> PLZ answer BOTH questions!!

Alexxx [7]

Answer:

The answer to your question is:

12) C

13) AT = 29

Step-by-step explanation:

12)

Data

A (6, -3)

B (-6, 19)

midx = (x1 + x2) / 2 midy = (y1 ´y2) / 2

midx = ( 6 - 6) / 2 midy = (-3 + 19) / 2

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midx = 0 midy = 8

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13)

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3 years ago