MATHEMATICS COLLEGE

HELP PLEZ TRIGONOMETRY!

Answers

Answer 1

Answer:

$(2 \sin ^(2) \alpha-1)/(\sin \alpha+\cos \alpha) = sin \alpha - cos \alpha$

Solution:

Given that we have to simplify:

$(2 \sin ^(2) \alpha-1)/(\sin \alpha+\cos \alpha)$ ---- eqn 1

We know that,

$sin^2 x = 1 - cos^2 x$

Substitute the above identity in eqn 1

$(2\left(1-\cos ^(2) \alpha\right)-1)/(\sin \alpha+\cos \alpha)$

Simplify the above expression

$(2-2 \cos ^(2) \alpha-1)/(\sin \alpha+\cos \alpha)$

$(1-2 \cos ^(2) \alpha)/(\sin \alpha+\cos \alpha)$ ------- eqn 2

By the trignometric identity,

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

Substitute the above identity in eqn 2

$((\sin \alpha+\cos \alpha)(\sin \alpha-\cos \alpha))/(\sin \alpha+\cos \alpha)$

Cancel the common factors in numerator and denominator

$((\sin \alpha+\cos \alpha)(\sin \alpha-\cos \alpha))/(\sin \alpha+\cos \alpha)=\sin \alpha-\cos \alpha$

Thus the simplified expression is:

$(2 \sin ^(2) \alpha-1)/(\sin \alpha+\cos \alpha) = sin \alpha - cos \alpha$

Related Questions

PLEASE help me please
Can someone plz help me wit this?
Solve x -2/3(3x - 4) + 3x = 5/6 is x -19/6, 11/6, 21/6, 29/6
So this is the question: Meg has 7/8 jug of orange juice. How many 1/2 jug servings can Meg get from that jug? Please help me!
In the first quadrant you start at (6, 10) and move 6 units right and 4 units down what point will you end up with

im ading and subtracting rational expression.my question is 5 is the numerator 2x -1 is the denominator + 6x +7 and 1 -4x squared

Answers

It's my method of solving this type of account, i get the denominators and multiply them by the fractions, then you cut the denominators, any questions just ask, i don't think that it was clarifying:

(2x-1) . (1-4x^2) . (5/2x-1) + (2x-1) . (1-4x^2) . (6x/1-4x^2) =
-> (1-4x^2) . 5 + (2x-1) . 6x =
-> 5 - 20x^2 + 12x^2 - 6x =
-> -8x^2 - 6x + 5 = 0

Delta = (-6)^2 - 4.(-8).5
Delta = 36 + 160 = 196

x' = - (-6) + sqroot(196) / 2.(-8)
x' = 6 + 16 / -16
x' = 22/-16 (simplifying by 2) = -11/8

x'' = 6 - 16 / -16 = -10/-16 (simplifying by 2)
x'' = 5/8

Can Someone please explain how to solve this. The directions say, "Solve the system by graphing. Then check your solution."

Answers

Try this suggested solution (see the attached picture, the answer is [-2;1]).

1 step to drow the graph required in the condition;

2 step to find intersection point (this is the A point);

3 step, check stage, to solve the system of two equations.

4 to compare the results in step 2 and step 3.

Find the volume, I really need help, thank you!!

Answers

the area of the base
$(4 * 6) / 2 = 24 / 2 = 12$

the volume
$12 * 6 = 72$

the answer is 72 in^3

good luck

Find the diameter, radius, area and circumference of the circle. Show your work.

Answers

Step-by-step explanation:

Radius:6ft

Diameter:12ft

Area:

$\pi {r}^(2) = \pi {6}^(2) = \n = 113.097336 = 113.1. {ft}^(2)$

circumference:

$2\pi * r = 2\pi * 6 = \n = 37.6991118 = 37.7 \: ft$

The table shows data for orders of cheese. Multiply each number of pounds of cheese in the table below by its frequency.Drag the tiles to complete the table. The first one is done as an example. Each tile may be used once, more than once, or not at all.

123456

Pounds Frequency Multiplication
1
4
1
4

4
4
1
1

3
4
3
4

8
8
1
1
4
1
1
4

4
4

Answers

Answer:

Part One:

Pounds Frequency Multiplication

1/4 4 1

3/4 8 6

1 1/4 4 5

1 1/2 2 3

Part Two:

The total number of pounds of cheese ordered is 15 pounds

Find the components of the vertical force Bold Upper FFequals=left angle 0 comma negative 4 right angle0,−4 in the directions parallel to and normal to the plane that makes an angle of StartFraction pi Over 3 EndFraction π 3 with the positive x-axis. Show that the total force is the sum of the two component forces.

Answers

Answer:

$F_p = < - √(3) , -3 >\n\nF_o = < √(3) , -1 >$

Step-by-step explanation:

- A plane is oriented in a Cartesian coordinate system such that it makes an angle of ( π / 3 ) with the positive x - axis.

- A force ( F ) is directed along the y-axis as a vector < 0 , - 4 >

- We are to determine the the components of force ( F ) parallel and normal to the defined plane.

- We will denote two unit vectors: ( $u_p$ ) parallel to plane and ( $u_o$ ) orthogonal to the defined plane. We will define the two unit vectors in ( x - y ) plane as follows:

- The unit vector ( $u_p$ ) parallel to the defined plane makes an angle of ( 30° ) with the positive y-axis and an angle of ( π / 3 = 60° ) with the x-axis. We will find the projection of the vector onto the x and y axes as follows:

$u_o$ = < cos ( 60° ) , cos ( 30° ) >

$u_o = < (1)/(2) , (√(3) )/(2) >$

- Similarly, the unit vector ( $u_o$ ) orthogonal to plane makes an angle of ( π / 3 ) with the positive x - axis and angle of ( π / 6 ) with the y-axis in negative direction. We will find the projection of the vector onto the x and y axes as follows:

$u_p = < cos ( (\pi )/(6) ) , - cos ( (\pi )/(3) ) >\n\nu_p = < (√(3) )/(2) , -(1)/(2) >\n$

- To find the projection of force ( F ) along and normal to the plane we will apply the dot product formulation:

- The Force vector parallel to the plane ( $F_p$ ) would be:

$F_p = u_p(F . u_p)\n\nF_p = < (1)/(2) , (√(3) )/(2) > [ < 0 , - 4 > . < (1)/(2) , (√(3) )/(2) > ]\n\nF_p = < (1)/(2) , (√(3) )/(2) > [ -2√(3) ]\n\nF_p = < -√(3) , -3 >\n$

- Similarly, to find the projection of force ( $F_o$ ) normal to the plane we again employ the dot product formulation with normal unit vector ( $u_o$ ) as follows:

$F_o = u_o ( F . u_o )\n\nF_o = < (√(3) )/(2) , - (1)/(2) > [ < 0 , - 4 > . < (√(3) )/(2) , - (1)/(2) > ] \n\nF_o = < (√(3) )/(2) , - (1)/(2) > [ 2 ] \n\nF_o = < √(3) , - 1 >$

- To prove that the projected forces ( $F_o$ ) and ( $F_p$ ) are correct we will apply the vector summation of the two orthogonal vector which must equal to the original vector < 0 , - 4 >

$F = F_o + F_p\n\n< 0 , - 4 > = < √(3), -1 > + < -√(3), -3 > \n\n< 0 , - 4 > = < √(3) - √(3) , -1 - 3 > \n\n< 0 , - 4 > = < 0 , - 4 >$ .. proven

Other Questions

Determine a region of the xy-plane for which the given differential equation would have a unique solution whose graph passes through a point (x0, y0) in the region. (x2 + y2)y' = y2 1. A unique solution exists in the region y ≥ x. 2. A unique solution exists in the entire xy-plane. 3. A unique solution exists in the region y ≤ x. 4. A unique solution exists in the region consisting of all points in the xy-plane except the origin.5. A unique solution exists in the region x2 + y2 < 1.

Please help thanks!!

The surface of a mountain is modeled by the equation h(x, y) = 5000 - 0.001x² - 0.004y². A mountain climber is at the point (500, 300, 4390). In what direction should the climber move in order to ascend at the greatest rate?

What sample size, including the 20 observations in the initial study, would be necessary to have a confidence of 95.44 percent that the observed time was within 4 percent of the true value?