1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
Sav [38]
3 years ago
10

URGENT! Describe step by step how to find the following equations.

Mathematics
1 answer:
yuradex [85]3 years ago
8 0

Answer:

1. x = 45°

2. x = 330°

3. x = 105°

4. x = 30°

5. x = 60°

6. x = 30° or x = -45° (315°) or x = 45°

Step-by-step explanation:

1. For

cos x = sin x

∴ sin x/(cos x) = 1 = tan x

Hence, x = tan⁻¹1 = 45°

2. For

csc(x) + 3 = 1

∴ csc(x) = 1 - 3 = -2

Which gives sin x = -1/2

∴ x = sin⁻¹(-1/2) = -30° = 360 +(-30) = 330 °

3. For

cot(3x) = -1

∵ cot(3x) = 1/(tan(3x))

Hence, 1/(tan(3x)) = -1

∴ tan(3x) = -1

3·x = tan⁻¹(-1) = -45° = 360 + (-45) = 315°

Which gives, x = -45/3 = -15° or x = 105°

4. For

2·sin²(x) + 3·sin(x) = 2

We put sin(x) = y to get

2·y² + 3·y = 2 or 2·y² + 3·y - 2 =0

Factorizing gives

(2·y -1)(y+2) =0

∴ y = 1/2 or y = -2

That is, sin(x) = 1/2 or sin(x) = -2

Hence, x = sin⁻¹(1/2) = 30° or x = sin⁻¹(-2) = (-π/2 + 1.3·i)

∴ x = 30°

5. For

4cos²(x) = 3 we have;

cos²(x) = 3/4

cos(x) = √(3/4) = (√3)/2

∴ x = cos⁻¹((√3)/2) = 60°

6. For

4·sin³(x) + 1 = 2·sin²(x) + 2·sin(x)

We put sin(x) = y to get;

4·y³ + 1 = 2·y² + 2·y which gives;

4·y³ + 1 - (2·y² + 2·y) = 0 or 4·y³ -2·y² - 2·y + 1 = 0

Factorizing gives;

\frac{(2x-1)(2x+\sqrt{2}) )(2x-\sqrt{2})}{2} =0

Therefore, x = 1/2 or x = -(√2)/2 or (√2)/2

Therefore, sin(x) = 1/2 or -(√2)/2 or (√2)/2

That is x = sin⁻¹(1/2) = 30 or sin⁻¹(-(√2)/2) = -45 or sin⁻¹((√2)/2) = 45.

You might be interested in
Select the coordinate point that is a solution of equations. 2x+y=7; 3x-4y=5
grandymaker [24]

Answer:

D (3,1)

Step-by-step explanation:

solving simultaneous equations

Arrange equations

2x+y=7

3x-4y=5

make y side cancell by addition by multiplying by 4 and 1 as shown

4{2x+y=7}

1{3x-4y=5}

8x+4y=28

3x-4y=5

11x=33

x=33/11=3

substitute for x=3 in 3x-4y=5

9-4y=5

4=4y

y=1

4 0
3 years ago
Read 2 more answers
Solve the equation for z <br>5z-8=32<br>A. z=4<br>B. z=4.8<br>C. z=6<br>D. z=8​
nadezda [96]

Answer:

Z=8 is the answer

Step-by-step explanation:

first, you add 8 to both sides which leaves you with 5z=40. then after that you divide both sides by 5 which leaves you with 5/5z = 40/5. then buy dividing 5 by 5 its leaves you with 1 which is equal to z because blank variables equal 1. On the other side if the equation 40 by 5 is 8 so that leaves you with z=8

5 0
2 years ago
Read 2 more answers
Quadrilateral BCDE is a rhombus. What is DE?<br> D<br> с<br> 9z<br> E<br> 2+72<br> B
aleksklad [387]

Answer:

DE = 81

Step-by-step explanation:

The sides of a rhombus are congruent , thus

9z = z + 72 ( subtract z from both sides )

8z = 72 ( divide both sides by 8 )

z = 9

Then

BC = 9z = 9 × 9 = 81

Since the sides are congruent, then DE = 81

6 0
3 years ago
jar of jelly contains 510 grams of jelly. There are about 26 servings in one jar. How much is one serving?
harkovskaia [24]

Answer: 19.615

Step-by-step explanation:

510 ÷ 26 = 19.615

4 0
3 years ago
Rx.gfgddhkhgccjykfdclycuktfktcl
Korolek [52]

Answer:

hi I see you are a beginner

this place is for questions and answers

not this that you are posting

3 0
3 years ago
Other questions:
  • What is the intersection of the sets A = {3, 4, 7, 8, 13} and B= {3, 7, 10, 13, 17}
    5·2 answers
  • What is the axis of symmetry for f(x) = 2x2 − 4x + 5?
    12·2 answers
  • What is 9,999,999 times 24
    7·1 answer
  • Susan is writing a linear equation for the cost of her cell phone plan. In the first month, she talks for 52 minutes and is char
    9·1 answer
  • Brett and Max are diving. Brett is 34 feet below the surface and Max is 25 feet below the surface. How many feet above Brett isM
    9·2 answers
  • Keisha is riding her bike on Bayview Bike path. Keisha‘s bike got a flat tire 2/3 of the way down the path, so she had to stop.
    14·1 answer
  • Determine whether the congruence is true or false.<br> 12 ≡ 10 mod 5
    12·1 answer
  • 8 oranges between 4 people. How many oranges will each person get?
    8·2 answers
  • what is an equation in the point-slope form of the line that passes through (-3,-1) and has a slope of 2?
    7·1 answer
  • What 2 numbers add to get 29 but when you subtract you get 1?
    11·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!