All categories

2 years ago

How do I solve these trigonometric equations!!?

1 answer:

3 0

<span>1) (sin x)(cos x) = 0 This means that either sin x = 0, or cos x = 0. Sin x = 0 when x = 0 or pi. cos x = 0 when x = pi/2 or 3pi/2. 2) cos2x + 2cosx + 1 = 0 First, expand cos2x. Simple trigonometric identity states that cos2x = (cos x)^2 - (sin x)^2.Now, substituting this equation, we get cos2x + 2cosx + 1 = (cos x)^2 - (sin x)^2 + 2cosx + 1. Note that we can now utilize the identity (cos x)^2 = 1 - (sin x)^2 to obtain (cos x)^2 + 2cosx + 1 - (sin x)^2 = 2(cos x)^2 + 2(cos x) = 0. Now, we can see that 2(cos x)^2 + 2(cos x) = 2(cos x)(cos x + 1) = 0. This is true when cos x = 0 or cos x + 1 = 0. Cos x = 0 when x = pi/2 or 3pi/2. cos x = -1 when x = pi. Therefore, x = pi/2, pi or 3pi/2.</span>

You might be interested in

Try to sketch by hand the curve of intersection of the parabolic cylinder y = x2 and the top half of the ellipsoid x2 + 7y2 + 7z

vovikov84 [41]

Plug $y=x^2$ into the equation of the ellipsoid:

$x^2+7(x^2)^2+7z^2=49$

Complete the square:

$7x^4+x^2=7\left(x^4+\dfrac{x^2}7+\dfrac1{14^2}-\dfrac1{14^2}\right)=7\left(x^2+\dfrac1{14}\right)^2+\dfrac1{28}$

Then the intersection is such that

$7\left(x^2+\dfrac1{14}\right)^2+7z^2=\dfrac{1371}{28}$

$\left(x^2+\dfrac1{14}\right)^2+z^2=\dfrac{1371}{196}$

which resembles the equation of a circle, and suggests a parameterization is polar-like coordinates. Let

$x(t)^2+\dfrac1{14}=\sqrt{\dfrac{1371}{196}}\cos t\implies x(t)=\pm\sqrt{\sqrt{\dfrac{1371}{196}}\cos t-\dfrac1{14}}$

$y(t)=x(t)^2=\sqrt{\dfrac{1371}{196}}\cos t-\dfrac1{14}$

$z=\sqrt{\dfrac{1371}{196}}\sin t$

(Attached is a plot of the two surfaces and the intersection; red for the positive root $x(t)$ , blue for the negative)

4 0

3 years ago

A Crayon is shown here.

Aleks04 [339]

The volume of the single crayon is 89.5 cm³, then the total volume of the crayons will be 2148 cm³. Then the correct option is D.

<h3>What is Geometry?</h3>

It deals with the size of geometry, region, and density of the different forms both 2D and 3D.

A Crayon is shown here.

There are 24 crayons in a box.

The approximate total volume of the crayons will be

Total Volume of crayons = 24 × volume of the single crayon

The crayon is the combination of the cone and the cylinder

Then the volume of the single crayon (V₁) will be

$\rm V_1 = \left ( \dfrac{1}{3} \times \pi \times r^2 \times h \right ) + \left ( \pi \times r^2 \times h \right )\\\\\rm V_1 = \left ( \dfrac{1}{3} \times \pi \times 1.5^2 \times 2 \right ) + \left ( \pi \times 1.5^2 \times 12 \right )\\\\V_1 = 4.712 + 84.82\\\\V_1 = 89.535 \approx 89.5$

Then the Total volume will be

Total volume = 24 × 89.5

Total volume = 2148 cm³

More about the geometry link is given below.

brainly.com/question/7558603

#SPJ1

3 0

1 year ago

What is 46.2 x 10 negative 2=

Nutka1998 [239]

The Answer is -924.

4 0

3 years ago

Answer pls so i can pass

Leto [7]

Answer: rounded: 2400

60 * 40

Actual: 2508

Step-by-step explanation:

8 0

3 years ago

Read 2 more answers

Plz some one help me

sveta [45]

9 games

You can get this by multiplying each percentage by the total number of games to see what they have to expect.

.55*180 = 99 games (red team)

.60*180 = 108 games (blue team)

Now subtract the blue team expectation from the red team.

108 - 99 = 9 games.

6 0

3 years ago