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Trigonometry
Trigonometry is a field of mathematics. It is the study of triangles. Trigonometry includes planar trigonometry, spherical trigonometry, finding unknown values in triangles, trigonometric functions, and trigonometric function graphs.
3,810 Questions
What is 216 degrees converted into radians?
180 degrees = pi radians( 3.141592.... radians) .
Hence
216/180 = x radians / pi radians.
Algebraically rearrange
x radians = 216 x pi / 180
x = 3.769911.... radians
one over root of 2 or (1/square root of 2) or 1/1.414213562 or 0.707106781
What is the formula for volume of a cone?
The formula is V = 1/3BH when B equals the area of the base and H equals the height of the cone. For example, if the area of the base is three cm2, and the height is four cm, then the volume is four cm3 because three (area of the base) times four (the height of the figure) divided by three (times 1/3) equals four cm3 (volume is always calculated in cubic units).
V = 1/3 (Base area) (Height) OR V= 1/3 (pi)r2h
How do you find the inverse log of a number?
Let x and y be any real numbers:
log x = y
x = log inv (y) = 10^y
Example:
pH =13.22 = -log [H+]
log [H+] = -13.22
[H+] = inv log (-13.22) = 10^(-13.22)
[H+] = 6.0 x 10-14 M
FINDING ANTILOGARITHMS using a calculator (also called Inverse Logarithm)
Sometimes we know the logarithm (or ln) of a number and must work backwards to find the number itself. This is called finding the antilogarithm or inverse logarithm of the number. To do this using most simple scientific calculators,
- enter the number,
- press the inverse (inv) or shift button, then
- press the log (or ln) button. It might also be labeled the 10x (or ex) button.
- Example 5: log x = 4.203; so, x = inverse log of 4.203 = 15958.79147..... (too many significant figures)
There are three significant figures in the mantissa of the log, so the number has 3 significant figures. The answer to the correct number of significant figures is 1.60 x 104. - Example 6: log x = -15.3;
so, x = inv log (-15.3) = 5.011872336... x 10-16 = 5 x 10-16 (1 significant figure)
Natural logarithms work in the same way:
- Example 7: ln x = 2.56; so, x = inv ln (2.56) = 12.93581732... = 13 (2 sig. fig.)
Application to pH problems:
- Example 8: What is the concentration of the hydrogen ion concentration in an aqueous solution with pH = 13.22? pH = -log [H+] = 13.22
log [H+] = -13.22
[H+] = inv log (-13.22)
[H+] = 6.0 x 10-14 M (2 sig. fig.)
It is a mathematical equation that allows you to "solve" a triangle (find all length and angle values), if you know 2 sides and an included angle, or all three sides. It doesn't have to be a right triangle. You can find the cosine on a calculator easily.
c2 = a2 + b2- 2ab cos C
C = included angle
c = side opposite angle C (c)
a = side a
b = side b
The cosine law relates the length of the sides of a triangle to one of the angles in the triangle. If the triangle is labelled with vertices A, B, C with usual notation for edges (ie a is the side opposite the vertex A, so not touching A) and if x is the angle at vertex C then the cosine law says (c^2)=(a^2)+(b^2)-2abcos(x)
What is the value of x in ax2 bx c0?
ax2 + bx + c = 0 , find the value of x .
b2-4ac>o x is real (2 different values will solve)
b2-4ac=o -> a double root (a single real number will solve it)
x=real numbers.
b2-4ac<0
x= two complex number roots (either pure imaginary or a complex number with real and imaginary components)
How are sines and cosines used in meteorology?
In trigonometry sines and cosines are used to solve a mathematical problem. And sines and cosines are also used in meteorology in estimating the height of the clouds.
I think first you calculate the area of the triangular face. If you forgot that's ok. The formula is A= bxh divided by 2 which is the same as the area of a triangle is base multiplyed by height and divided by two. Then you need to know the length of the prism(the length of the rectangle)and multiply them together. So your calculation should look like this: Triangular face- A=bxh divided by 2 let's say that the base of the triangle is 5 cm and the height is 12cm Length of prism- let's say the length is 25 cm A=bxh divided by 2 A=5 x 12 divided by 2 A = 20 divided by 2 A = 30 cm squared 30 x 25 = 750cm squared( little 2)
What is the formula for the volume of a triangular prism?
The general way to find the volume for any shape is the formulaV=Bh (volume equals base times height). The specific formula used to find the volume of a triangular prism is V=1/2(or 0.5)bhh (volume equals one half or 0.5 times base times height times height again.
What year of high school is trigonometry usually taken?
there is an introat the end of grade ten but there is a real unit in grade eleven trigonometry is usaully taken during geometry and parts of pre/calculus. Its about 10th and/or 11th grade!
Where online can you find Geometry worksheets?
Now a days, learning has become much easy. You can get help with concepts of math online. You can search for math help or geometry help online and get a learning from online.
Try typing in "cool math 4 kids" in your search engine. That's a great website for stuff like that, but I can't think of their address right now.
If you split a rectangle into 2 triangles what type of triangle do you get?
A 30-60-90 right triangle
As the bowl is hemispherical in share, tilting it does not change the shape of the water, and so its depth remains the same.
When the bowl has been tilted 35o, the distance the lip of the bowl has been lowered can be found using the Sine ratio. This can be subtracted from the height the lip was above the bottom the the bowl (namely the radius of the bowl) to find how deep the water is.
The angle is 35o.
The hypotenuse is the radius of the bowl.
The opposite side is the unknown drop.
sine 35o = drop/20 cm
⇒ drop = 20cm x sine 35o
≈ 11.47 cm
height = radius - drop
≈ 20 cm - 11.47 cm
= 8.53 cm
What is six trigonometric ratios of 45 degrees?
sin(45) = cos(45) = 1/sqrt(2)
tan(45) = cot(45)= 1
csc(45) = sec(45) = sqrt(2)
What is life without trigonometry?
Life would be awesome!
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As "awesome" as the Middle Ages in fact - would you really want that sort of life? And you use the Internet to tell us think it would be awe-inspiring? Try using the word "awful" instead!
Trigomometry does NOT exist as an isolated discipline. It is one of very many branches of mathematics, without which, just think - very limited science, engineering and architecture, no navigation to speak of, no frequency-analysis so no electronics and acoustics... Without the engineering we'd have nothing to generate the electricity or use it in anyway - including your computer!
How do you differentiate Tan2x?
Chain Rule:
let u=2x and y=tan(u)
du/dx = 2 and dy/du = sec^2(u)
dy/dx = du/dx x dy/du
multiply them together and replace u=2x into the equation..
therefore dy/dx = 2(sec^2(2x))
hope that helps.
Why tan A 90 degree is not solve?
I am not sure what "tan A 90 degree" means.
tan(90 degrees) is an expression that is not defined and so cannot be solved.
One way to see why that may be so is to think of tan(x) = sin(x)/cos(x).
When x = 90 degrees,
sin(90) = 1 and cos(90)= 0 that tan(90) = 1/0 and since division by 0 is not defined, tan(90) is not defined.
What is the largest angle of a triangle with sides of 14 cm 8.5 cm and 9 cm?
The largest angle of the triangle will be opposite its largest side and by using the Cosine Rule it works out as 106.23 degrees.
What is the difference of plane and spherical triangles?
The main difference is that the plane triangle is on a flat surface while the spherical triangle is on the surface of a sphere. One consequence is that the angles of a plane triangle sum to 2*pi radians (180 degrees) while those on a sphere sum to more than 2*pi radians.
Where did the concept of geometry first originate?
The exact date is not clear but it is probably when early stone-age people decided to chip away at flints to make sharp knives or arrowheads for hunting.
