Use trig identities to show that sec θ − cos θ = tanθ (sin θ)

Answers

Answer 1

Use [tex]\sec\theta = \dfrac{1}{\cos{\theta}}[/tex]  to get

    [tex]\sec\theta -\cos{\theta}= \dfrac{1}{\cos{\theta}}-\cos(\theta})[/tex]

Then find a common denominator:

    [tex]\dfrac{1}{\cos{\theta}}-\cos(\theta}) = \dfrac{1}{\cos{\theta}}-\dfrac{\cos^2\theta}{\cos\theta}[/tex]

But now make that one fraction:

    [tex]\dfrac{1}{\cos{\theta}}-\dfrac{\cos^2\theta}{\cos\theta} = \dfrac{1 - \cos^2\theta}{\cos{\theta}}[/tex]

But that's just sin^2 on the top

    [tex]\dfrac{1 - \cos^2\theta}{\cos{\theta}} = \dfrac{sin^2\theta}{\cos{\theta}} = \dfrac{sin\theta\cdot sin\theta}{\cos{\theta}}[/tex]

Split that fraction up:

    [tex]=\dfrac{ sin\theta}{\cos{\theta}}\cdot sin\theta[/tex]

And tan = sin/cos

    [tex]=\tan\theta\cdot sin\theta[/tex]


Related Questions

OMGGG PLS HELP ME WITH THIS QUESTION PLS PLS PLS!!! WILL MARK BRAINEST AND PLS PLS PLS DO EXPLAIN!!!

Answers

Answer:

38

Step-by-step explanation:

-(5×-7-3)

-(-35-3)

-(-38)

38

Help pls
what is the slope intercept form of (-1,8) and (3,6)

Answers

Answer: y = 1/2x+15/2

Step-by-step explanation:

If you need any more help let me know!! I will try to answer every question you post!

I have no idea how to find multiple angles i was only taught how to find one..

Answers

The sum of all angles must equal 180°. Since you already have two angles for the larger triangle, all you need to do to find m < x is by subtracting m < 63° and m < 36° from 180°:

m < x = 180° - m < 63° - m < 36°
m < x = 81°

Therefore, < x = 81°

For the smaller triangle (acute), what you could do to find m < z is by subtracting m < x from 180°. We can do it that way because < x and < z are supplementary angles whose sum add up to 180°.

m < z = 180° - m < x
m < z = 180° - m < 81°
m < z = 99°

Therefore, < z = 99°

Lastly, to find m < y, subtract m < 13°and m < z° from 180°:

m < y = 180° - m < z° - m < 13°

m < y = 180° - m< 99° - m< 13°
m < y = 68°


Therefore, the measure of the following angles are:

< x = 81°
< y = 68°
< z = 99°

Answer:

36+63+_=180

Step-by-step explanation:

just add up everything in the smaller triangle to get 180

then ignore the line inside of the bigger triangle and repeat the first step, but only just look at the bigger one! that is how to do it, but I won't give the answer, good luck! ;)

Tomas and Tasha were hiking at a speed of 3.5 mph on their way back they were tired and their speed was 2 mph how long was the route if the way back took them 1 hour and 30 minutes longer (in miles)

Answers

Answer: 7 miles

Step-by-step explanation:

To get the length of the route use the expression for speed,

Distance = Speed × Time

Length of the route is 7 miles.

It's given in the question,

Speed of Tomas and Tasha initially = 3.5 mph

Therefore, distance travelled by both with the speed of 2 mph one way will be,

Distance = 3.5t [Here, t = time ]

Speed of both while coming back = 2 mph

And the time taken = t + (1 hour 30 minutes)

= (t + 1.5) hours

Therefore, distance travelled while coming back = Speed × Time

= 2(t + 1.5)

Since, length of the route is same both ways,

3.5t = 2(t + 1.5)

3.5t = 2t + 3

3.5t - 2t = 3

1.5t = 3

t = 2 hours

Now substitute the value of t in the expression to get the distance of the route,

Distance = 3.5t

= 3.5 × 2

= 7 miles

Therefore, route was 7 miles long.

Answer:

7

Step-by-step explanation:

look at answer

Write this equation in slope-intercept form by isolating the y-variable.
12x = 4y

Answers

I believe this is it

please check the picture!!

find the indefinite integral of:

Answers

Answer:

x = 23

Step-by-step explanation:

2x+5+6x^2-4x+3x^4-6x^2+4x^4+7x

Answers

The answer is: 7x^4+5x+5

Write the side length of the square as a square root. Is the side length a rational number? Explain. a= 121

Answers

Answer:

yes

Step-by-step explanation:

Note that [tex]121=11^2[/tex].

The side length of the square with an area of [tex]121=11^2[/tex] will be [tex]\sqrt{11^2}[/tex].

Recall that [tex]\sqrt{a^2}=a[/tex], so the side length is [tex]\sqrt{11^2}=11[/tex]. [tex]11[/tex] is clearly rational because it's an integer, so the answer is [tex]\boxed{yes}[/tex], it is rational.

[tex]\red{ \boxed{ \blue{ \tt{Help\:Me}}}}[/tex]​

Answers

Answer:

You go to a job and get $352.15 a day. How much would you make in a month?

Answer: 352.15 x 31= 10,916.65

Hope this helps ^^

what is the midpoint of 0.1 and 0.2

Answers

The answer is definitely 0.15

Determine the slope of this graph. Please get right. And ill add extra points.

Answers

Answer:

1/2

Step-by-step explanation:

Slope is the rise over the run.  This means the difference in the y values over the difference in the x values.

The two points on the graph are (2,-2) and ( -6, -6 ).

The difference in the y values is a total of 4 units.

The difference in the x values is a total of 8 units.

The slope would then be 4/8 which simplifies to 1/2.

The line slants upward from left to right so the slope is positive.

Solve this pls

6i<5i+3u

Answers

i < 3u

Step-by-step explanation:

6i < 5i + 3u

6i - 5i < 3u

i < 3u

Drag each label to the correct location.
Use what you’ve learned about proportional relationships to classify these equations as direct variation, inverse variation, or neither.
PLEASE HELPPP

Answers

Answer:

Step-by-step explanation:

is 3x² - 4ab + 2 a polynomial?

Answers

Answer:

Yes it is a polynomial.

Step-by-step explanation:

3x² - 4ab + 2 is quadratic polynomial, since it has the highest power / degree of 2.

Note : -

Types of polynomials :

Linear Polynomial ( degree 1 )Quadratic Polynomial ( degree 2 )Cubic Polynomial ( degree 3 )Quartic Polynomial ( degree 4 )

Answer:

[tex]4394[/tex]

Step-by-step explanation:

the bird is

Billy read an average of 2.5 magazines each week during the year.



Write an equation that represents the amount of magazines that he read (y) per week (x).

Answers

Answer: y=2.5x+

Step-by-step explanation:

I dont know the rest because the question is worded wrong

The equation that represents the number of magazines that he read (y) per week (x) will be y = 2.5x.

What is a linear equation?

A relationship between two or more parameters that, when shown on a graph, produces a linear model. The degree of the variable will be one.

The linear equation is given as,

y = mx + c

Where m is the slope of the line and c is the y-intercept of the line.

Billy read an average of 2.5 magazines each week during the year.

The equation that represents the number of magazines that he read (y) per week (x) will be

y = 2.5x

The equation that represents the number of magazines that he read (y) per week (x) will be y = 2.5x.

More about the linear equation link is given below.

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Which of the following equations represents a line that passes through the points (-10, -9)(−10,−9) and (10,-1)(10,−1)?
I. y+1=-\frac{2}{5}(x-10)y+1=−
5
2

(x−10)
II. 2x-5y=252x−5y=25

Answers

Answer:

y = 2/5x - 5

Step-by-step explanation:

(-10,-9) and (10,-1)

Slope: (-1 - - 9) / ( 10 - - 10)

Slope = 8/20 = 2/5

b = -9 - (2/5(10)

b = -5

The equation of the line that passes through the point (−10,−9) and (10,-1) is; y = 2/5x - 5

What is the Point-slope form?

The equation of the straight line has its slope and given point.

If we have a non-vertical line that passes through any point(x1, y1) and has a gradient m. then general point (x, y) must satisfy the equation

y-y₁ = m(x-x₁)

Where x₁ - x coordinate, y₁ - y coordinate, m - slope

Slope: (-1 - - 9) / ( 10 - - 10)

m = Slope = 8/20 = 2/5

Now intercept;

b = -9 - (2/5(10)

b = -5

Now Write the equation as

y = 2/5x - 5

Hence, the equation of the line that passes through the point (−10,−9) and (10,-1) is; y = 2/5x - 5

Learn more about equations here;

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what is 46+56+3+17+30=

Answers

Answer:

The answer to your question is 152

Step-by-step explanation:

46+56+3+17+30= 152

I hope this helps!

Answer:

152

Step-by-step explanation:

46+56= 102. 102+3= 105. 105+17= 122. 122+30= 152

How do you find percentages?

Answers

Answer:

obtained number divided by total number multiply by 100%.

· Definition of Percentages

Mathematically, percentages are either numbers or ratios that are expressed as fractions of 100. They are usually denoted as "%" or simply "percent." They may be further represented as simple fractions or as decimal fractions. An example of a percentage is 65% or 65 percent.  The term percentage was formed from two words, “per” and “cent.” Cent is a word with Latin and French origin that means "hundred," and "percent" means "per hundred." For example, 90 percent (or 90%) means 90 out of 100 while 50 percent (or 50%) means 50 out of 100 or half of a whole.

1. Determine the initial format of the number to be converted to a percentage

The number to be converted to a percentage can either be in the decimal or fraction format. A good example of a decimal number is 0.57, which may be the calculated ratio of the values you are comparing, while an example of a fraction is 3/20. The initial format will determine the next mathematical process to be carried out on the number.

2. Carry out a mathematical process on the number to be converted to a percentage

If the number to be converted to a percentage is a decimal number like 0.57, you may not need to do anything to it before you go to the next step. However, if it is a fraction like 3/20, you should first divide the numerator (3 in this case) by the denominator (20 in this case) to get a decimal number.

3. Multiply the result of the mathematical process by 100

If you are required to convert a decimal number like 0.57 to a percentage, you are to simply multiply it by 100. That is, 0.57 x 100 = 57. Therefore, 0.57 as a percentage = 57% or 57 percent. Another example of converting a decimal to a percentage is 0.03 x 100 = 3% or 3 percent.

However, if you are required to convert 3/20 to a percentage, you should divide 3 by 20 = 0.15. Then multiply 0.15 by 100 = 15% or 15 percent.

Another example is if you are to convert 5/10 to a percentage, you should divide 5 by 10 = 0.5. Then, multiply 0.5 by 100. Therefore, 0.5 x 100 = 50% or 50 percent.

Order these numbers from the least to the greatest. 7.618, 7.681, 7.6801, 7.0681

Answers

Answer:

7.0681, 7.618, 7.6801, 7.681

Step-by-step explanation:

from the least (smallest) to the greatest (largest)

7.0681, 7.618, 7.6801, 7.681

Solve the equation –x^2 -6x=-2x^2 to the nearest tenth.

Answers

Answer:

The answer is x = 3

Step-by-step explanation:

edge2020

When you have two perpendicular lines that cross at the midpoint, what is the degrees if the angles ?
A( 180
B(90
C(360

Answers

Answer:

B) 90

Step-by-step explanation:

Perpendicular lines always meet at a 90 degree angle.

Answer:

B{90 but it depends which way like it could be A{180 but i'm pretty sure B

Step-by-step explanation:

common since

Which property of addition is shown here? (4+5)+6=4+(5+6)

Answers

Answer:

I am pretty sure it is Associative property of addition

Step-by-step explanation:

a teacher is making bags of different colors of modeling clay. the table shows the amount of each color she has avalible. each color will be divided into 3/16 pound bags. how many more bags of purple can she make then yellow?

Answers

Using the subtraction operation, the number of purple bags is 3 more than the number of yellow bags.

Amount of each color available :

Amount of purple color = 64

Amount of Yellow bags = 48

Amount of color in pound required per bag = [tex]\frac{3}{16} [/tex]

Number of Purple bags :

Amount of color required per bag × Amount of purple color

Number of purple bags = [tex]\frac{3}{16} \times 64 = 12[/tex]

Number of Yellow bags :

Amount of color required per bag × Amount of Yellow color

Number of yellow bags = [tex]\frac{3}{16} \times 48 = 9[/tex]

Now we find the difference between the number of Purple and Yellow bags :

Number of purple bags - Number of yellow bags

Difference = 12 - 9 = 3 bags

Therefore, there are 3 more purple bags than Yellow bags.

Learn more :https://brainly.com/question/18109354

Is a list of numbers and each number is called a term of the sequence

Answers

Answer:

Terms are positive or negative single mathematical expressions.

Step-by-step explanation:

Consider the matrices.

Answers

Answer:

Attached

Step-by-step explanation:

the moons gravity is weaker than that of the earth

if a feather dropped on the moon falls 81.25 cm in 1 second, calculate the acceleration due to gravity on the moon, expressed in m/s/s

Answers

We want to find the moon's gravitational acceleration.

With the given information, we will see that the gravitational acceleration on the moon is: g = 1.625 m/s^2

We know that in a place with a gravitation acceleration g, if you drop something from a height H, the position equation of that object will be given by:

p(t) = (-g/2)*t^2 + H

In this case, we know that a feather falls 81.25cm in one second.

First, we can define H = 0 (because we can put the zero of the position where we want to)

Then if after one second the feather falls 81.25cm = 0.8125 meters, we need to solve:

p(1s) = -0.8125 m = (-g/2)*(1s)^2

Where the negative sign comes because the feather "falls" and we define the negative position as below.

Also notice that we did a change of units from centimeters to meters, by knowing that:

100cm = 1m

then:

81.25cm = 0.8125m

Now we just need to solve:

-0.8125 m = (-g/2)*(1s)^2

0.8125 m = (g/2)*(1s)^2

2*0.8125 m = (g)*1s^2

1.625 m = g*1s^2

(1.625 m)/(1 s^2) = g

We then can conclude that the moon's gravitational acceleration is:

g = 1.625 m/s^2

If you want to learn more,, you can read:

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Jon and Becky measured the circle-shaped part of a sun they drew on the sidewalk.

The diameter of the circle is 67 centimeters. What is the approximate area of the circle? (Use 3.14 for .)

Answers

Answer:

the area of the circle is 3,523.86

Step-by-step explanation:

In the morning, the temperature was–10°C. By the afternoon, it had risen to–2°C. What was the change in temperature from the morning to the afternoon?To solve the problem, Luke subtracted–2–(–10) and came up with an answer of 8°C. Is Luke correct? Why or why not?

Answers

luke is correct because -2 - (-10) =8 (because when you subtract a negative from a negative it equals a positive)

Jim is going from Town A to Town B. Town B is located at (-4, 5). He makes a stop at his friend’s house, which is halfway along the trip. What are the coordinates of his stop?

Answers

Answer:

tạo độ của anh ấy dừng là:

Step-by-step explanat ion(:-2,2.5)

The price of an item is $45.00. After a discount, the price is $38.25. What is the percent of the discount?
Answer correctly and I will give brainliest

Answers

Answer:

=15

Step-by-step explanation:

45-x% *45=38.25

(-45) x/100=38.5-45

(-45)x/100=(-6.75)

x=6.75 * 100/45

=15

The percent of the discount is 15.

It is required to find the percent of the discount.

What is percentage?

A part of a whole expressed in hundredths a high percentage of students attended. Also the result obtained by multiplying a number by a percent the percentage equals the rate times the base.

Given:

Let the discount percent be x%

When the price of $45 is reduced by x%, we get $38.25.

So,

45 − x % ∗ 45 = 38.25

− 45 x /100 = 38.25 − 45

− 45 x /100 = − 6.75

x = 6.75 ∗ 100 /45

x= 15

Therefore, the percent of the discount is 15.

Learn more about percentage here:

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