Write each of the following as a function of theta.
1.) sin(pi/4 - theta) 2.) tan(theta+30°)

Answers

Answer 1

Step-by-step explanation:

Let x represent theta.

[tex] \sin( \frac{\pi}{4} - x ) [/tex]

Using the angle addition trig formula,

[tex] \sin(x - y) = \sin(x) \cos(y) - \cos(x) \sin(y) [/tex]

[tex] \sin( \frac{\pi}{4} ) \cos(x) - \cos( \frac{\pi}{4} ) \sin(x) [/tex]

[tex]( \frac{ \sqrt{2} }{2}) \cos(x) - (\frac{ \sqrt{2} }{2} )\sin(x) [/tex]

Multiply one side at a time

Replace theta with x , the answer is

[tex] \frac{ \sqrt{2} \cos(x) }{2} - \frac{ \sin(x) \sqrt{2} }{2} [/tex]

2. Convert 30 degrees into radian

[tex] \frac{30}{1} \times \frac{\pi}{180} = \frac{\pi}{6} [/tex]

Using tangent formula,

[tex] \tan(x + y) = \frac{ \tan(x) + \tan(y) }{1 - \tan(x) \tan(y) } [/tex]

[tex] \frac{ \tan(x) + \tan( \frac{\pi}{6} ) }{1 - \tan(x) \tan( \frac{\pi}{6} ) } [/tex]

Tan if pi/6 is sqr root of 3/3

[tex] \frac{ \tan(x) + ( \frac{ \sqrt{3} }{3} ) }{1 - \tan(x) (\frac{ \sqrt{3} }{3} ) } [/tex]

Since my phone about to die if you later simplify that,

you'll get

[tex] \frac{(3 \tan(x) + \sqrt{3} )(3 + \sqrt{3} \tan(x) }{3(3 - \tan {}^{2} (x) } [/tex]

Replace theta with X.


Related Questions

solution for the inequality 6x +9 ≤ 27

Answers

Answer:

6x + 9 = 27

       -9     -9

6x = 18           Now divide both sides by 6

/6      /6            so the answer is 3

Step-by-step explanation:

please help with this!

Answers

Answer:

a) HK

b) EF

c) ∠J

d) ∠E

e) JKH

solve using the Pythagorean theorem.
need urgent help​

Answers

Answer:

y = 7

Step-by-step explanation:

Mathematically, according to the Pythagoras’ theorem;

The square of the length of the hypotenuse of a right triangle is equal to the sum of the squares of the two other sides

The hypotenuse is the side that faces the right angle and it is represented by the square root of 85 here

Thus, we have it that;

(√85 )^2= 6^2 + y^2

85 = 36 + y^2

y^2 = 85-36

y^2 = 49

y = √49

y = 7

Cherlyn moves houses her old house is 3 kilometers from her new house how many meters is it from the old house to the new house?

Answers

Answer:

3,000 meters

Step-by-step explanation:

1 Kilometer = 1,000 meters

1,000 meters x 3 Kilometers = 3,000 meters

Hopefully this helps :3 Sorry if wrong :( plz mark brainiest if correct :D Your bootiful/handsome! Have a great day luv <3

-Bee~

PLEASE HELP!! I'll give the correct answer brainliest and 5 stars

Answers

Answer:

C 150/30 (Your answer)

Step-by-step explanation:

bc 150 BLUE marbles and 30 RED marbles so ur right

Answer:

The answer is C

Step-by-step explanation:

Its asking for the ration of BLUE to RED. In ratio you always do the first unit/object so its asking for blue then red so its 150(blue/30(RED)

Find each value.
p(4,4)
p(6,3)
p(9,5)

Answers

Answer:

the probability: (4,4) it is certain to happen. (6,3) it is not likely nor unlikely

because it is half. (9,5) it is likely to happen.

Step-by-step explanation:

(4,4) is the value (6,3) and (9,5) are not it

An investor has an account with stock from two different companies. Last year, her
stock in Company A was worth $1060 and her stock in Company B was worth $4290.
The stock in Company A has increased 15% since last year and the stock in Company
B has increased 20%. What was the total percentage increase in the investor's stock
account? Round your answer to the nearest tenth (if necessary).

Answers

Answer:

Final Answer: 19%

Step-by-step explanation: I had the same question, I risked my life and got it wrong for you to get the answer

In ANOP, the measure of _P=90°, NO = 49 feet, and OP = 19 feet. Find the measure
of N to the nearest degree.
O
N
49
19

Answers

Answer:23

Step-by-step explanation:

Answer:

the answer is 23

Step-by-step explanation:

the measures of the side of a triangle are 4√2 cm, 4√2 cm qnd 8√2 cm. what is the perimeter of the triangle?​

Answers

Answer:

[tex]16\sqrt{2}[/tex]

Step-by-step explanation:

Add up all the sides to get the perimeter:

[tex]4\sqrt{2} + 4\sqrt{2} +8\sqrt{2} = 16\sqrt{2}[/tex]

On Anti-Bullying day, 378 Chenery Middle School (CMS) students wore Orange. If this represents 45% of the student population, how many students are enrolled at CMS?

Answers

Remember part/whole...
Your answer should be 840 students

Why are 4(5) and 20 equivalent expressions?

Answers

Answer:

because 4 to the power of 5 is 5 x 5 x 5 x 5 and that equals 20

and the next number is 20

Step-by-step explanation:

Solve the equation.
Show your steps.
3x + 265 = 4

Answers

Answer:

x = -87

Step-by-step explanation:

Isolate the variable, x. Note the equal sign, what you do to one side, you do to the other. Do the opposite of PEMDAS.

PEMDAS is the order of operation and stands for:

Parenthesis

Exponents (& Roots)

Multiplication

Division

Addition

Subtraction

~

First, subtract 265 from both sides of the equation:

3x + 265 (-265) = 4 (-265)

3x = 4 - 265

3x = -261

Next, divide 3 from both sides:

(3x)/3 = (-261)/3

x = -261/3

x = -87

x = -87 is your answer.

~

Answer:

If you're looking for the value of x, it's -87.

Step-by-step explanation:

1. Subtract 265 from both sides

3x+265-265 = 4-265 = 3x = -261

2. Divide by 3 to get the variable by itself

3x/3 = -261/3. = -87

x = -87

Hope this helps

Can someone help me ASAP plz

Answers

Answer:

[tex]\boxed{\text{\sf \Large 138.6 mm^2 $}}[/tex]

Step-by-step explanation:

Area of rectangle

[tex]15 \times 5=75[/tex]

Area of circle (semi-circle+semi-circle)

[tex]r=(15-3-3) \div 2 = 4.5[/tex]

[tex]\pi \times 4.5^2=20.25\pi[/tex]

Add both areas

[tex]20.25\pi +75[/tex]

[tex]20.25 \times 3.14 +75=138.585[/tex]

Given that a sports team ends a season with 12 wins and 8 losses, what is the probability that the team had 5 runs of wins? * 0.083 0.225 0.315 0.442 0.557

Answers

Answer:

Step-by-step explanation :

examine this graph. what are the y-intercept and slope of this line HELP PLLZ

Answers

Answer:

y-intercept is basically the y variable. Looking on the graph above your y-intercept is 2. To find slope it is rise / run. In the graph your slope is -2/3.

Hope this helps, thank you :) !!

The required slope of the given equation of the line shown in the graph is -2/3.

Given that,
A graph of the line has been shown, we have to determine the slope of the line.

What is the slope of the line?

The slope of the line is a tangent angle made by line with horizontal. i.e. m =tanx where x in degrees.

Here,

Since the slope of the line is measure of the angle inclined with the axis
As from observation, the line is passing from points (0,2) and (3, 0).
The slope of the line,
m = (y₂ - y₁) /  (x₂ - x₁)
m = (0 - 2) / (3 - 0)
n = -2/3

Thus, the required slope of the given equation of the line shown in the graph is -2/3.

Learn more about slopes here:

https://brainly.com/question/3605446

#SPJ2

A model railroad set was originally priced at $60, but Oliver waited to buy it until the model railroad set was on sale for 50% off. If he paid 10% sales tax on the sale price, how much did he pay in total?

$

Answers

Answer:

$33

Step-by-step explanation:

60 * 50% = 30

30 *10% = 3

30 + 3 = $33

Answer:

Step-by-step explanation:

$33

Step-by-step explanation:

60 * 50% = 30

30 *10% = 3

30 + 3 = $3

what is a^2 + 10a+24

Answers

Answer:

Step-by-step explaintation

a2 + 10a = 24

10a + a2 = 24

10a + a2 = 24

Solving for variable 'a'.

Reorder the terms:

-24 + 10a + a2 = 24 + -24

Combine like terms: 24 + -24 = 0

-24 + 10a + a2 = 0

Factor a trinomial.

(-12 + -1a)(2 + -1a) = 0

Set the factor '(-12 + -1a)' equal to zero and attempt to solve:

Simplifying

-12 + -1a = 0

Solving

-12 + -1a = 0

Move all terms containing a to the left, all other terms to the right.

Add '12' to each side of the equation.

-12 + 12 + -1a = 0 + 12

Combine like terms: -12 + 12 = 0

0 + -1a = 0 + 12

-1a = 0 + 12

Combine like terms: 0 + 12 = 12

-1a = 12

Divide each side by '-1'.

a = -12

Simplifying

a = -12

if you help me I’ll love you forever <3

Answers

Answer:

translation

Step-by-step explanation:

because a reflection across the x-axis is not right, and neither is across the y-axis. The triangle was also not rotated 90 degrees. It was translated 8 units to the right and 4 units up.

Identify the domain and range of the function.​

Answers

The domain is everything on the left(under x) and the range is everything on the right (under y)

Brainliest plz

How pink is blue?? How blue is pink??

Answers

The simple answer to this question is purple. However, because of the nature of the color pink, it can vary based on that. Purple is secondary color itself, as it’s the byproduct of red and blue. However, because there is some white in there from the pink, we are going to get a variety of shades.

For what value of x is AABC - ADEF?
HELP PLEASE!!

Answers

Answer:

A) x = 12

Step-by-step explanation:

4x-6 = 42

4 = 48

x = 12

7x+10 = 94

7x = 82

x = 12

Sam answered 5 questions
incorrectly on atest. For each
incorrect answer 3 points were
deducted from a score of 100.
What was Sam's Score?

Answers

Answer:

If Sam incorrectly answered 5 questions, and for each question 3 points were deducted, a total of 5x3, or 15 points were deducted.

Sam scored an 85.

Let me know if this helps!

11 = 7 – 5x
Please help!

Answers

Answer:

the answer is x=-4/5

Step-by-step explanation:

hoped I helped:)

Answer:

-4/5

Step-by-step explanation:

11=7+-5x

11=-5x+7

-5x+7=11

-5x+7-7=11-7

-5x=4

-5x/-5=4/-5

Suppose 2.7 gallons of water come out of a faucet each minute. Find the amount of water coming out in 1.2 minutes.

Answers

Answer:

3.24 gallons

Step-by-step explanation:

2.7x1.2=3.24

Answer:

3.24

Step-by-step explanation:

1.2 is 1 whole plus 20/100

so 1*2.7=2.7

.2*2.7=0.54

0.54+2.7= 3.24

st is tangent to q find the value of r

Answers

Answer:

r = 7

Step-by-step explanation:

The angle between the tangent ST and the radius QS at the point of contact is 90° , then

Δ QST is right

Using Pythagoras' identity in the right triangle

(r + 18)² = r² + 24² , that is

r² + 36r + 324 = r² + 576 ( subtract r² from both sides )

36r + 324 = 576 ( subtract 324 from both sides )

36r = 252 ( divide both sides by 36 )

r = 7

6. Given that g(x) is the inverse of f(x)...
a. f(x) = 3x + square root x + 3; find g(2)
b. f(x) = e^x; find g'(e3)

Answers

Answer:

sub 2 lazarbeam... yeet yeet yeet

8 less than or equal to -2x+16​

Answers

The Answer is 8 ≤ -2x+16.

an amusement park charges $4.25 for admission, plus $1.50 for each ride ticket. Chase has $30 to spent on admission and ride tickets

Answers

Answer:

he went on 16 rides and paid for 2 admission

Step-by-step explanation:

he went on 16 rides and paid for 2 admission

A farmer sells 6.6 kilograms of apples and pears at the farmer's market. 3 5 of this weight is apples, and the rest is pears. How many kilograms of pears did she sell at the farmer's market?

Answers

Answer:

If 3 5 is 3/5 then 2.64 would be the answer

Step-by-step explanation:

convert 3/5 to a percentage which is 60%. find 60% of 6.6

tell whether x and y are proportional

Answers

Answer:

Yes b/c y = 12x

Step-by-step explanation:

y = 12x

Other Questions
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