sin cos 23

sin cos 22

sin cos 21

sin cos 20

sin cos 19

sin cos 18

sin cos 17

sin cos 16

sin cos 15

sin cos 14

sin cos 13

sin cos 12

sin cos 11

sin cos 10

sin cos 9

sin cos 8

sin cos 7

sin cos 6

sin cos 5

sin cos 4

sin cos 3

sin cos 2

sin cos 1

1/sinx+1/(sin(x-3pi/2))=4sin(7pi/4-x)

-3x^2+15=0

-3x^2+15=0
<=> -3x^2+3.5 =0
<=> -3(x^2-5)=0
<=> x^2=5

5x^2-20x=0

5x^2-20x=0
<=>5x(x-4)=0
<=> 1. 5x=0 <=> x=0
2. x-4=0 <=> x=4

3x^2+9x=0

3x^2+9x=0
<=>3x(x-3)=0
<=> 1. 3x=0 <=> x=0
2. x-3=0 <=> x=3

7x^2-5x=0

7x^2-5x=0
<=>x(7x-5)=0
<=> 1. x=0
2. 7x-5=0 <=> x=5/7

3x^2-6x=0

3x^2-6x=0
<=>3x(x-6)=0
1.<=>3x=0 <=>x=0
2.<=>x-6=0 <=> x=6


equation level 2, math-online

cosxcos2xcos4xcos8x=1/16

cosxcos2xcos4xcos8x=1/16
+)sinx=0 => VT#VP => VN
+)sinx#0
Nhân cả hai vế của phương trình với sinx ta được:
<=>sinxcosxcos2xcos4xcos8x=1/16
<=>sin2xcos2xcos4xcos8x=1/8
<=>sin4xcos4xcos8x=1/4
<=>sin8xcos8x=1/2
<=>sin16x=sinx

trigonometric,math-online

Sin^3 (2x).cos6x+sin6x.cos^3 ( 2x)= 3/8

Sin^3 (2x).cos6x+sin6x.cos^3 ( 2x)= 3/8
<=>cos6x.(3sin2x-sin6x)/4 +sin6x.(3cos2x-cos6x)/4 = 3/8
<=>sin2x.cos6x+cos2x.sin6x = 1/2
<=>sin(2x+6x) = 1/2
<=>sin8x =1/2

trigonometric,math-online

cos10x+2cos^24x+6cos3xcosx=cosx+8cosxcos^3x

trigonometric,math-online

How to calculate sales tax

Exercises # 1:

You buy a car for 20,000 dollars and pay 5 % in tax. How much is tax?

Tax = 20,000 times 5% = 20,000 times 0.05

Tax = 20,000 times 0.05 = 1,000 dollars.

The cost with tax is 20,000 + 1000 = 21,000

Exercises # 2:

You buy a house for 400,000 dollars and pay a tax of 6 %. How much is tax?

Tax = 400,000 times 6 %

Tax = 400,000 times 0.06 = 24,000 dollars

The cost with tax is 400,000 + 24,000 = 424,000 dollars.

Exercises # 3:
The list price of a scientific calculator is 100 dollars.If you get a price discount of 15 % and pay 5 % for tax, what is the actual cost of your calculator?

First, find the price after the discount

Discount = 100 times 15 % = 100 times 0.15 = 15

Sale price = 100 - 15 = 85 dollars

Tax paid = 85 times 5 % = 85 times 0.05 = 4.25

Actual cost = 85 + 4.25 = 89.25 dollars.

You will get the same answer if you compute the tax paid first and then compute the discount.

Common geometry formulas

Here, we provide you with common geometry formulas for some basic shapes

---

Rectangle:



Perimeter = l + l + w + w = 2 × l + 2 × w

Area = l × w

---

Square:



Perimeter = s + s + s + s = 4 × s

Area = s²

---

Parallelogram:



Perimeter = a + a + b + b = 2 × a + 2 × b

Area = b × h

---

Rhombus:



Perimeter = b + b + b + b = 4 × b

Area = b × h

---

Triangle:



Perimeter = a + b + c

Area = (b × h)/2

---

Trapezoid:



Perimeter = a + b + c + d

---

Circle:



Perimeter = 2 × pi × r or Perimeter = pi × d

Area = pi × r² or Area = (pi × d²)/4

Basic math test

Solve the following problems


1. Write this number in words

157802 ______________________________________________

2. Round 36,993 to the nearest thousands____________________________

3. Round 6.724 to the nearest hundredth____________________________

4. 324 times 87______________________________

5. 81.32 times 0.3214

6. Divide 89 into 4356_________________________________

7. Find the greatest common factor of 24 and 76_______________________

8. Find the least common factor of 12 and and 36_______________________

9. Circle the numbers that are prime.

      2       5       8       13       17       18       21       93       117

10. Tell if the fraction on the left is less or greater than the fraction on the right. Use < or >

11. Add the following fractions:

12. Tell if the decimal on the left is less or greater than the decimal on the right. Use < or >

5.43123        5.43013

13. What is the perimeter and area of a rectangle with sides equal to 5 inches and 7 inches?

Perimeter = __________________ inches       area=____________________

14. 35% of 40 is ____________

15. What percent of 80 is 100? _____________________

16. Rename 2/5 as a percent_______________________

17. Describe in your own words what it means for 2 lines to be parallel. Show a drawing.

18. Solve for n: 6n + 12 = 6

19. What is the volume of the following figure?____________________

20. What is the elapsed time between 5:45 AM and 4:10 PM?

21. Measure the following angles with a protractor__________     __________

22. What is the perimeter and area of a circle with diameter equal to 5 cm?

Perimeter = __________________       area=____________________

23. 25 cm = __________mm        1250 g = ___________kg        25 mL = _______________L

24. Convert the difference of 25 min. 14 sec and 4 min. 30 sec in seconds__________________

25. A scale of 1:20 is used to make the drawing of a car. If the length of the drawing is 10 inches, what is the real length of the car?

Real length__________________

26. Write these numbers in scientific notation

2300000000__________________              0.00024___________________

27. 12 feet = ____________ yards            2 gallons = _____________ pints

28. -2 + -6 =________            -4 + 3 = _________            5 − - 2 = _________

29. -2 × 4 =__________           -6 ÷ - 2=____________

30. What is the absolute value of -3?

Types of angles

There are many different types of angles. We will define them in this lesson.

Acute angle:

An angle whose measure is less than 90 degrees. The following is an acute angle.



Right angle:

An angle whose measure is 90 degrees. The following is a right angle.



Obtuse angle:

An angle whose measure is bigger than 90 degrees but less than 180 degrees. Thus, it is between 90 degrees and 180 degrees. The following is an obtuse angle.



Straight angle

An angle whose measure is 180 degrees.Thus, a straight angle look like a straight line. The following is a straight angle.



Reflex angle:

An angle whose measure is bigger than 180 degrees but less than 360 degrees.The following is a reflex angle.

Adjacent angles:

Angle with a common vertex and one common side. <1 and <2, are adjacent angles.

Complementary angles:

Two angles whose measures add to 90 degrees. Angle 1 and angle 2 are complementary angles because together they form a right angle.

Note that angle 1 and angle 2 do not have to be adjacent to be complementary as long as they add up to 90 degrees



Supplementary angles:

Two angles whose measures add to 180 degrees. The following are supplementary angles.



Vertical angles:

Angles that have a common vertex and whose sides are formed by the same lines. The following(angle 1 and angle 2) are vertical angles.



When two parallel lines are crossed by a third line(Transversal), 8 angles are formed. Take a look at the following figure



Angles 3,4,5,8 are interior angles

Angles 1,2,6,7 are exterior angles

Alternate interior angles:

Pairs of interior angles on opposite sides of the transversal.

For instance, angle 3 and angle 5 are alternate interior angles. Angle 4 and angle 8 are also alternate interior angles.

Alternate exterior angles:

Pairs of exterior angles on opposite sides of the transversal.

Angle 2 and angle 7 are alternate exterior angles.

Corresponding angles:

Pairs of angles that are in similar positions.

Angle 3 and angle 2 are corresponding angles.

Angle 5 and angle 7 are corresponding angles