MATHEMATICS HIGH SCHOOL

Having trouble with trigonometry , please help.

CSCx (1 + SINx) = 1 + CSCx

prove the identity

Answers

Answer 1
Answer: Remember that the cosecant is the reciprocal of the sine.  CSC(x) = 1/SIN(x).

Now operate on the left side, and see if you can make it look like the right side:

CSCx (1 + SINx)

Substitute for CSCx :

(1/SINx) (1 + SINx)

Multiply them:

1/SINx + SINx/SINx 
which is the same as  1/SINx + 1
which is the same as CSCx + 1,
and that's the right side of the identity, so you proved it.

Related Questions

A cotton candy holder is shaped like a cone. The height is 12 in., and the diameter is 12 in. What is the volume of the holder? Use 3.14 to approximate pi, and express your final answer to the nearest tenth.. ______in3
Which of the following is an equivalent form of the compound inequality -22 > -5x - 7 -3? A)-5x - 7 < -22 and -5x - 7 -3B)-5x - 7 < -22 and -5x - 7 -3C)-5x - 7 > -22 and -5x - 7 -3D)-5x > -22 and -7 -3
The ratio of males to females ata party is 3:5. There are twelve more females than males. Howmany people are at the party?
To paint a house, two painters are hired. The first painter can paint the house in ten hours. The second painter will need six hours to paint the entire house. If the two painters start painting at 8:00 am, at what time will they finish painting the house?
What is 48 divided by one sixth

The function below shows the number of car owners f(t), in thousands, in a city in different years t:f(t) = 0.25t2 − 0.5t + 3.5

The average rate of change of f(t) from t = 2 to t = 6 is ______ thousand owners per year.

Answers

Answer:

1.5 thousand owners per year.

Step-by-step explanation:

Number of car owners is represented by the function as

f(t) = 0.25t² - 0.5t + 3.5

Where 't' is time in years.

Now we have to find the rate of change of f(t) from t = 2 to t = 6

or (f(6)-f(2))/(6-2)

f(6) = 0.25 × 36 - 0.5 × 6 + 3.5

     = 9 - 3 + 3.5

     = 9.5

f(2) = 0.25 × 4 - 0.5 × 2 + 3.5

     = 1 - 1 + 3.5

     = 3.5

Now average rate of change (f(6)-f(2))/(6-2)=(9.5-3.5)/(6-2)

=(6)/(4)

= 1.5 thousand owners per year.

A 9-kg of mangoes for 12$_____per kg

Answers

If 9kg costs 12$, then a single kg costs around 1.3$

This is done with a simple proportion

9 : 12 = 1 : X
x = 12/9
x = 1.33

You are going to have a swimming pool put your back yard this summer. The dimensions of the pool are going to be 15 ft by 30 ft. There is going to be a concrete walkway around the outside of the pool, but they are not sure how wide it will be. The design of the pool, including the walkway, is shown below.

Answers

The perimeter of a shape is the sum of the all visible side lengths of the shape. The perimeter of the pool including the walkway is 90 + 8x

Given that:

Length = 15

Width = 30

Let the width of the walkway be x.

The dimension of the pool including the walkway is calculated by adding the dimension of the pool to the width of the walkway (on both sides):

So, we have:

Length = 15 + x + x

Length = 15 + 2x

Width = 30 + x + x

Width = 30 + 2x

The perimeter (P) of the walkway is then calculated using:

P = 2 * (Length + Width)

This gives:

P = 2 * (15 + 2x + 30 + 2x)

Collect like terms

P = 2 * (15 + 30+ 2x + 2x)

P = 2 * (45+ 4x)

Open brackets

P = 2 * 45+ 2 * 4x

P = 90+ 8x

Hence, the perimeter of the pool including the walkway is 90 + 8x (see attachment)

Read more about perimeters at:

brainly.com/question/6465134

A total of $8,000 is deposited in two simple interest accounts. In one account, the annual simple interest rate is 5%, and on the second account, the annual simple interest rate is 6%. How much should be invested in each account so that the total annual interest earned is $450?

Answers

you need to invest $3000 at the 5% interest rate and invest $5000 the 6% interest rate to get a total annual interest of $450

you have 160 boxes of cookies, in each case you can pack 8 boxes. how many cases will be packed from these cookies ?

Answers

1 case=8 boxes of cookies   and we have 160 boxes
160/8=20
we will have 20 cases

WHATS THE SLOPE OF THE RED LINE AND THE BLUE LINE?? and is the line parallel?? PLEASE I NEED THIS DONE

Answers

The line is Nor Parnell since it is side waysblkejsdjsjnw

Answer:

The slopes of both lines are 2/3, and since they have different y-intercepts they are parallel.

Step-by-step explanation:

In order to find slope, you need to find the rise and run of the line, since slope is rise/run. Lets use the red line as an example: There are two points , (0,1) and (-2,-1) where there are solid points. Once you locate solid points, you can then count how many units up or down (rise) and how many left or right (run). If you do this on paper the lines should form a right triangle with the line as the hypotenus. Since we went up 2, right 3, the slope would be 2/3.

Hope this helps :)
Other Questions
What is the percentage multiplier to increase a quantity by 22%? a. 0.22 b. 1.22 c. 22 d. 0.78
Please help. I do not understand and I have limited time to do so
Which is a recursive formula for the sequence 99.4, 0, –99.4, –198.8, where f(1) = 99.4?
A phone company uses the equation y=0.15x+10 to find y the monthly charge for a customer sending x text messages. How many text messages are sent if the monthly charge is $77.50?