trigonometric identities

Trigonometric Identities

Answers

Answer 1

With 180° < θ < 270°, we know that both cos(θ) < 0 and sin(θ) < 0.

Then from the Pythagorean identity, it follows that

sin²(θ) + cos²(θ) = 1   ==>   sin(θ) = -√(1 - cos²(θ))

and so

sin(θ) = -√(1 - (-8/13)²) = -√105/13

Recall the double angle identity for sine:

sin(2θ) = 2 sin(θ) cos(θ) = 2 (-√105/13) (-8/13) = 16√105/169


Related Questions

(c) 63 divided by 3 = 21 , Show how you use this to work out 0.63 divided by 0.3.

Answers

Answer:

0.63 ÷ 0.3 = 63 x 10^-2 ÷ 3 x 10^-1 = 63 / 3  x 10^(-2--1) = 21 x 10^-1 = 2.1

Answer:

2.1.

Step-by-step explanation:

63/3 = 21

0.63 = 63 / 100

and 0.3 = 3 / 10

so 0.63/0.3 = 63 /100 / 3/10 = 63/100 * 10/3

= 63/3 / 10

So the answer is 21 / 10 = 2.1.

9 in.
13 in.
10 in
Drawing not to scale
b. 90 in?
45 in?
d. 292.5 in.
c. 32 in?
a.

Answers

Answer:

a, a, d

Step-by-step explanation:

44

The area (A) of a triangle is calculated as

A = [tex]\frac{1}{2}[/tex] bh ( b is the base and h the perpendicular height )

Here b = 10 and h = 9 , then

A = [tex]\frac{1}{2}[/tex] × 10 × 9 = 5 × 9 = 45 in² → a

45

The area (A) of a parallelogram is

A = bh ( b is the base and h the perpendicular height )

Here b = 2 and h = 4 , then

A = 2 × 4 = 8 m² → a

46

A = bh ( with b = 4 and h = 10 )

A = 4 × 10 = 40 m² → d

1+1=

please help me, this question is very difficult​

Answers

I think it’s 47743774367

Answer:

2 or tricky answer 11

What is the difference between-5 and 2

Answers

Answer:

7

Step-by-step explanation:

Going from -5 to 2 we get

1) -4

2) -3

3) -2

4) -1

5) 0

6) 1

7) 2

So, in total, there are 7 numbers between -5 and 2

what is 13.5/10 simplified

Answers

Answer:

27/20

Step-by-step explanation:

[tex]\frac{13.5}{10} = \frac{13.5 * 2}{10 * 2} = \frac{27}{20}[/tex]

13.5/20 simplified is 27/20

Parallelogram JKLM is shown. If KR=X+7, KM = 3x - 5. and JL = 4x - 10.
what is JR?
2 points
K
R
569
27°
72°
M

Answers

Answer:

Step-by-step explanation:

In a parallelogram, this one in particular:

KR = RM

JR = RL

We are looking in the end for the length of JR, but that means that we need to solve for x somehow to plug in the expression for JL, and then split that in half. Here's how we're going to go about it. I know that

KM = KR + RM, but since KR and RM are the same length, the equation becomes

KM = 2KR. Filling that in with the expressions I'm given for KM and KR:

3x - 5 = 2(x + 7) and

3x - 5 = 2x + 14 and

x = 19. Now I can find the length of JL:

JL = 4x - 10 so

JL = 4(19) - 10 and

JL = 66

Knowing that JR = RL and JL is 66 units long, JR = RL = 33 units each.

45.55 to 1 decimal place

Answers

Answer:

45.6

Step-by-step explanation:

45.55

We want to round to the tenths place

we look at the hundredths place

.x5  Since the number in the hundredths place is 5 or greater, we round up 1

45.55 becomes 45.6

Answer:

the answer is 45.6

Step-by-step explanation:

[tex]\sf{}[/tex]

♛┈⛧┈┈•༶♛┈⛧┈┈•༶

Can someone PLEASE answer the Algebra Question CORRECTLY BELOW!
Thank you, I will mark brainiest!

Answers

Answer:

There are 0.454 kg in one pound.

So, in 120 pounds there are 0.454 x 120 kgs.

This is equal to 54.48, and the answer is 54.48 kg.

Let me know if this helps!

Instructions: Find the missing side. Round your answer to the nearest
tenth.
15
66°
х
x
=

Answers

Answer:

x = 16.4

Step-by-step explanation:

Since this is a right triangle, we can use trig functions

sin theta = opp / hyp

sin 66 = 15/x

x sin 66 = 15

x = 15/sin 66

x=16.41954

Rounding to the nearest tenth

x = 16.4

Beverly fpund a magic bean. If she puts it in the soil , every single day it will grow 4 cm. After how many days will it be 14.56 meters tall

Answers

Answer:

364 days

Step-by-step explanation:

Magic bean will take 364 days to grow 14.56 m tall.

What is Unit Conversion?

A conversion factor exists as a ratio that expresses how many of one unit stand equal to another unit. For example, there exist 12 in. in 1 ft, 1609 m in 1 mi, 100 cm in 1 m, 60 s in 1 min, and so on.

Unit conversion exists as a multi-step procedure that involves multiplication or division by a numerical factor, choosing the accurate number of significant digits, and rounding.

First we need to convert the height in m into cm.

14.56 m=14.56*100=1456 cm

If it grows 4 cm in one day then:

It will take 1456/4=364 days (a year) to grow completely.

To know more about unit conversion refer:

https://brainly.com/question/6243489

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If the blue radius below is perpendicular to the chord AC which is. 14 units long, what is the length of the segment AB?

Answers

Answer:

C. 7 units

Step-by-step explanation:

The given parameters are;

The length of the chord of the circle, [tex]\overline{AC}[/tex] = 14 units

The orientation of the radius and the chord = The radius is perpendicular to the chord

We have in ΔAOC, [tex]\overline{AO}[/tex] = [tex]\overline{OC}[/tex] = The radius of the circle

[tex]\overline{OB}[/tex] ≅ [tex]\overline{OB}[/tex]  by reflexive property

The angle at point B = 90° by angle formed by the radius which is perpendiclar to the chord [tex]\overline{AC}[/tex]

ΔAOB and ΔCOB are right triangles (triangles having one 90° angle)

[tex]\overline{AO}[/tex] and [tex]\overline{OC}[/tex] are hypotenuse sides of ΔAOB and ΔCOB respectively and [tex]\overline{OB}[/tex] is a leg to ΔAOB and ΔCOB

Therefore;

ΔAOB ≅ ΔCOB, by Hypotenuse Leg rule of congruency

Therefore;

[tex]\overline{AB}[/tex] ≅ [tex]\overline{BC}[/tex] by Congruent Parts of Congruent Triangles are Congruent, CPCTC

[tex]\overline{AB}[/tex] = [tex]\overline{BC}[/tex] by definition of congruency

[tex]\overline{AC}[/tex] = [tex]\overline{AB}[/tex] + [tex]\overline{BC}[/tex] by segment addition postulate

∴ [tex]\overline{AC}[/tex] = [tex]\overline{AB}[/tex] + [tex]\overline{BC}[/tex] =  [tex]\overline{AB}[/tex] + [tex]\overline{AB}[/tex] = 2 ×  [tex]\overline{AB}[/tex]

∴  [tex]\overline{AB}[/tex] = [tex]\overline{AC}[/tex]/2

[tex]\overline{AB}[/tex] = 14/2 = 7

[tex]\overline{AB}[/tex] = 7 units.

Answer:

7 units

Step-by-step explanation:

if u can help be fast please​

Answers

A) 5 sides = 72.00

interior =108.00

B) 9 sides = 40.00

interior = 140.00

C) 15 sides = 24.00

interior = 156.00

D) 19 sides = 18.95

interior = 161.05

These are exterior angles right? y'know what I'll just put both

HELP ME PLS ITS PYTHAGOREAN THEOREM

Answers

Answer:

a= [tex]\sqrt{19}[/tex]

Step-by-step explanation:

Pythagorean Theorem: a^2+b^2=c^2

a^2+9^2=10^2

a^2+81=100

a^2=19

a=[tex]\sqrt{19}[/tex]

Answer:

b = 4.4 meters

Question 16 of 17
Which of the following best describes the graph below?

A. Independent variable
0 o a
B. A relation that is a function
C. A relation that is not a function
D. Dependent variable

Answers

The answer is B. It is a relation and also a function at the same time because it satisfies a specific domain

MATCH THE SYSTEM OF EQUATIONS ON THE LEFT WITH THE APPROPRIATE SOLUTION ON THE RIGHT

Answers

Answer:

Step-by-step explanation:

After a 20% reduction, you purchase a tv for $336. What was the price of the tv before the reduction?

Answers

Answer:

$420

.8 x = 336

x = 336/.8

X=$420

Step-by-step explanation:

Can someone please help me with my maths question​

Answers

Answer:

[tex]a. \ \dfrac{625 \cdot m}{27 \cdot n^{11}}[/tex]

[tex]b. \ \dfrac{x^{3 \cdot m - 2}}{y^{ 3 + n}}[/tex]

Step-by-step explanation:

The question relates with rules of indices

(a) The give expression is presented as follows;

[tex]\dfrac{m^3 \times \left (n^{-2} \right )^4 \times (5 \cdot m)^4}{\left (3 \cdot m^2 \cdot n \right )^3}[/tex]

By expanding the expression, we get;

[tex]\dfrac{m^3 \times n^{-8} \times 5^4 \times m^4}{\left 3^3 \times m^6 \times n^3}[/tex]

Collecting like terms gives;

[tex]\dfrac{m^{(3 + 4 - 6)} \times 5^4}{ 3^3 \times n^{3 + 8}} = \dfrac{625 \cdot m}{27 \cdot n^{11}}[/tex]

[tex]\dfrac{m^3 \times \left (n^{-2} \right )^4 \times (5 \cdot m)^4}{\left (3 \cdot m^2 \cdot n \right )^3}= \dfrac{625 \cdot m}{27 \cdot n^{11}}[/tex]

(b) The given expression is presented as follows;

[tex]x^{3 \cdot m + 2} \times \left (y^{n - 1} \right )^3 \div (x \cdot y^n)^4[/tex]

Therefore, we get;

[tex]x^{3 \cdot m + 2} \times \left (y^{n - 1} \right )^3 \times x^{-4} \times y^{-4 \cdot n}[/tex]

Collecting like terms gives;

[tex]x^{3 \cdot m + 2 - 4} \times \left (y^{3 \cdot n - 3 -4 \cdot n}} \right ) = x^{3 \cdot m - 2} \times \left (y^{ - 3 -n}} \right ) = x^{3 \cdot m - 2} \div \left (y^{ 3 + n}} \right )[/tex]

[tex]x^{3 \cdot m - 2} \div \left (y^{ 3 + n}} \right ) = \dfrac{x^{3 \cdot m - 2}}{y^{ 3 + n}}[/tex]

[tex]x^{3 \cdot m + 2} \times \left (y^{n - 1} \right )^3 \times x^{-4} \times y^{-4 \cdot n} =\dfrac{x^{3 \cdot m - 2}}{y^{ 3 + n}}[/tex]

Is the domain of an arithmetic sequence discrete or continuous? Is the range of an arithmetic sequence discrete or continuous?

Answers

Answer:

continuous, continuous

Step-by-step explanation:

The discrete domain are set of input variables that have numbers in an interval. A continuous domain has all numbers in an interval. The point representing the solution of an equation are distinct. The range of sequence is the merely a set of defines the sequence and is represented as X1, X2, X3, or N = 1, 2, 3.

(a/b)^x-1 = (b/a)^x-3​

Answers

Answer:

x = 2

Step-by-step explanation:

HELP ILL GIVE U BRAINLIEST

Answers

Answer:

-6 33/40

Step-by-step explanation:

[tex]2\frac{5}{8} = 2.625\\-2\frac{3}{5} = 2.6\\\\2.625 *-2.6 = -6.825\\\\-6.825 = -6\frac{33}{40}[/tex]

Best answer gets brainliest and 5 star

Answers

Answer:

d no.

Step-by-step explanation:

because in my my personal opinion the function shown on the graph has a smaller rate of change, but a higher starting point

The answer is A. Calculating the rate of change for the graph is 3 and that of the equation is 4. The starting point of the graph is -2 and that of the equation is 6.

Find the area of the shaded regions:

Answers

Answer:

18[tex]\pi[/tex]

[tex]\frac{80}{360} * 81 \pi[/tex]

Step-by-step explanation:

What is the value of the expression below when x=3
10x²- 7x + 10

Answers

Answer: 79

Concept:

Here, we need to understand the idea of evaluation.  

When encountering questions that gave you an expression with variables, then stated: "If x = a, y = b, z = c" (a, b, c are all constants), this means you should substitute the value given for each variable back to the expression.

Solve:

Given information

10x² - 7x + 10

x = 3

Substitute the value into the expression

= 10 (3)² - 7 (3) + 10

Simplify by multiplication

= 10 (9) - 21 + 10

= 90 - 21 + 10

Simplify by subtraction

= 69 + 10

Simplify by addition

= 79

Hope this helps!! :)

Please let me know if you have any questions

Answer:

92

Step-by-step explanation:

The variable 'x' shows up twice in this expression.  Replace each instance of 'x' with 3:

10(3)^2 - 7(3) + 10  =  10(9) - 21 + 19  =  92

Se desea pintar un cuadrado inscrito en una circunferencia de radio R=3cm como se muestra en la figura. Calcular el área del cuadrado

Answers

El área del cuadrado es de 3 centímetros cuadrados.

Dado que se desea pintar un cuadrado inscrito en una circunferencia de radio R=3cm como se muestra en la figura, para calcular el área del cuadrado se debe realizar el siguiente cálculo:

Radio = diámetro / 2 3 = X/2 X = 6Hipotenusa del triángulo interno: 6 cm

Aplicando teorema pitagórico: lado al cuadrado mas lado al cuadrado es igual a hipotenusa al cuadrado.

L^2 + L^2 = 62L^2 = 6L^2 = 6/2L = √ 3L = 1.732Área de un cuadrado = L x L = L^2 = 3

Por lo tanto, el área del cuadrado es de 3 centímetros cuadrados.

Aprende más en https://brainly.com/question/16405529

El área del cuadrado es de 18 centímetros cuadrados.  

El procedimiento de resolución se basa en conocer que la Medida de la Diagonal de un Cuadrado inscrito es igual a la Medida del Radio del Círculo, lo cual permite determinar el valor de la medida del Cuadrado en función del Radio del Círculo. Finalmente, determinamos el Área del Cuadrado mediante su fórmula conocida.

Dado que existe un cuadrado inscrito en un círculo, la medida de la diagonal del cuadrado es igual a la medida del radio del círculo. Además, conocemos que un cuadrado está formado por 4 triángulos rectángulos con configuración angular 45-45-90. Entonces, la medida del lado del cuadrado se calcula mediante la siguiente relación geométrica:

[tex]l = \sqrt{2}\cdot R[/tex] (1)

Donde:

[tex]R[/tex] - Radio del círculo, en centímetros.

[tex]l[/tex] - Longitud del lado del cuadrado, en centímetros.

Por otra parte, la ecuación de área del cuadrado es igual a:

[tex]A = l^{2}[/tex] (2)

Donde [tex]A[/tex] es el área del cuadrado, en centímetros cuadrados.

Si sabemos que [tex]R = 3\,cm[/tex], entonces el área del cuadrado es:

[tex]l = \sqrt{2}\cdot (3\,cm)[/tex]

[tex]l = 3\sqrt{2}\,cm[/tex]

[tex]A = (3\sqrt{2}\,cm)^{2}[/tex]

[tex]A = 18\,cm^{2}[/tex]

El área del cuadrado es de 18 centímetros cuadrados.  

He aquí una pregunta relacionada sobre el área del cuadrado: https://brainly.com/question/23915250

5x2y and 7xy2 are like terms.

True
False

Answers

Answer: False

The variable portions x^2y and xy^2 are slightly different, so that's why we don't have like terms here.

Answer:

False

Step-by-step explanation:

Like terms are those terms where they have the same variable

so here

5x2y variables are = 5x and 2y

7xy2 variables are = 7x and y2

you can observe that x variable is same but y variable is not same as 5x3y have 2y whereas 7xy2 have y2#

so the answer is FALSE

f(x) = (x - 5) (2x - 7) (7x - 3) has zeros at x = -3.5, x = 3/7, and x = 5.

what is the sign of f on the interval 3/7 < x < 5 ?

1. f is always positive on the interval.
2. f is always negative on the interval.
3. f is sometimes positive and sometimes negative on the interval.

Answers

The function f(x) will be sometimes positive and sometimes negative on the interval so option (3) will be correct.

What is a function?

A certain kind of relationship called a function binds inputs to essentially one output.

In other terms, a function is a relationship between variables, and the type of relationship that exists between the variables defines the function, such as y = sinx and y = x +6.

Given function is

f(x) = (x - 5) (2x - 7) (7x - 3)

The term (x - 5) will be negative if x < 5.

The term (2x - 7) will be negative if x<3.5

Let's say if x = 4 then (x - 5) will be negative but (2x - 7) will be positive and hence overall value will be negative.

But if x = 3 then (x - 5) will be negative and (2x - 7)  will also be negative and hence overall value will be negative

Hence the function f is sometimes positive and sometimes negative on the interval.

For more about the function

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Answer:

always negative the other guy was wrong because when you wrote 2x - 7 you meant 2x + 7 I know this because it’s on Khan Academy

Step-by-step explanation:

if x =2 y =3 find the value of x^2-xy^2+y^2​

Answers

Answer:

i hope it will help

Step-by-step explanation:

I did not get the equation so I solve it with two methods

When a new cellphone is put on the market, the demand each month can be described by the function C of t is equal to negative square root of the quantity t squared plus 4 times t minus 12 end quantity plus 3 where C (t) represents the demand of the cellphone (measured in millions of people) and the time, t, is measured in months. Which of the following solution(s) are valid for a positive demand? (7, 0) and (3, 0) (–6, 3) and (2, 3) (6, 3) (2, 3)

Answers

Answer:

(2, 3)

Step-by-step explanation:

Answer:

It is (2,3)

Step-by-step explanation:

Two hikers are miles apart and walking toward each other. They meet in hours. Find the rate of each hiker if one hiker walks mph faster than the other.

Answers

Answer:

where are the numbers

Step-by-step explanation:

How can this quadrilateral be classified?
Select each correct answer.
O trapezoid
O square
O rhombus
O parallelogram

Answers

Answer:

Rhombus, Square, Parallelogram :)

Step-by-step explanation:

I just did this question and I got the three answers above right. I hope this helps!

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