Which could be the value of the third side of a triangle with sides 3 and 4? A. 3 B. 7 C. 12 D. 20

Solve sin 0 + 1 = cos20 on the interval 0 ≤ 0 < 2pi. Show work please!

yan [13]

Answer:

$\theta=\frac{\pi}{2},\frac{3\pi}{2}\frac{2\pi}{3}\frac{4\pi}{3}$

Step-by-step explanation:

You need 2 things in order to solve this equation: a trig identity sheet and a unit circle.

You will find when you look on your trig identity sheet that

$cos(2\theta)=1-2sin^2(\theta)$

so we will make that replacement, getting everything in terms of sin:

$sin(\theta)+1=1-2sin^2(\theta)$

Now we will get everything on one side of the equals sign, set it equal to 0, and solve it:

$2sin^2(\theta)+sin(\theta)=0$

We can factor out the sin(theta), since it's common in both terms:

$sin(\theta)(2sin(\theta)+1)=0$

Because of the Zero Product Property, either

$sin(\theta)=0$ or

$2sin(\theta)+1=0$

Look at the unit circle and find which values of theta have a sin ratio of 0 in the interval from 0 to 2pi. They are:

$\theta=\frac{\pi}{2},\frac{3\pi}{2}$

The next equation needs to first be solved for sin(theta):

$2sin(\theta)+1=0$ so

$2sin(\theta)=-1$ and

$sin(\theta)=-\frac{1}{2}$

Go back to your unit circle and find the values of theta where the sin is -1/2 in the interval. They are:

$\theta=\frac{2\pi}{3},\frac{4\pi}{3}$

7 0

3 years ago

Mr. Rogers recorded the height of 15 students from two of his classes. Based on these samples, what generalization can be made?

Sati [7]

You are not giving enough information but in one of the calsses the average of student's height might be greater than the other class beacause one of the two classes needs to have 1 extra person than the other calss

6 0

3 years ago

What's Trey doing tomorrow?

Pavel [41]

Answer:

B

Step-by-step explanation:

He also is a point guard and has shoe game.

6 0

3 years ago

Read 2 more answers

What does parallelepiped focus on

charle [14.2K]

A parallelepiped focuses on three-dimensional figures formed by six parallelograms.

<h3>How to explain the parallelepiped?</h3>

A parallelepiped shape has the following features

They are three-dimensional figures
They are formed by 6 parallelograms
Opposite parallelograms are congruent

Think of a cube or a cuboid.

Notice that they contain squares and rectangles

A parallelepiped is to a parallelogram as a square is to a cube and a rectangle to a cuboid

Read more about parallelepiped at:

brainly.com/question/3050890

#SPJ11

7 0

2 years ago

Read 2 more answers

A 2 kg metal cylinder is supplied with 1600J of energy to heat it from 5°C to 13°C. What is the specific heat capacity of the me

Neporo4naja [7]

Answer:

$c = 100\,\frac{J}{kg\cdot ^{\circ}C}$

Step-by-step explanation:

According to the First Law of Thermodynamics, the heat received by the metal cylinder is equal to the change in the internal energy. That is:

$Q = \Delta U$

$Q = m \cdot c \cdot \Delta T$

The specific heat is clear in the previous expression and finally computed:

$c = \frac{Q}{m\cdot \Delta T}$

$c = \frac{1600\,J}{(2\,kg)\cdot (13^{\circ}C-5^{\circ}C)}$

$c = 100\,\frac{J}{kg\cdot ^{\circ}C}$

6 0

3 years ago