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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
The only difference is a phase shift of pi/2 radians (90 degrees), so there is no aprticular advantage in either.
Sine cubed plus cosine cubed divided by sine plus cosine?
[sin(x)^3 + cos(x)^3] / [sin(x) + cos(x)]
= [(sin(x) + cos(x))(sin(x)^2 - sin(x)cos(x) + cos(x)^2)] / [sin(x) + cos(x)]
***Now you can cancel a "sin(x) + cos(x)" from the top and bottom of the fraction. This makes the bottom of the fraction equal to 1. I am just going to write the next step without a 1 on the bottom of the fraction (x/1=x).
So now you just have:
= (sin(x)^2 - sin(x)cos(x) + cos(x)^2) *I'm going to move some terms around now. ~
Not doing any computation in this step.
= (sin(x)^2 + cos(x)^2 - sin(x)cos(x)) *Now we know that cos(x)^2 + sin(x)^2 = 1.
= 1 - sin(x)cos(x)
What is the Contribution of hipparchus to trigonometry?
Created the division of a circle into 360 degrees and made one of the first trigonometric tables for solving triangles.
sin2 + cos2 = 1
So, (1 - 2*cos2)/(sin*cos) = (sin2 + cos2 - 2*cos2)/(sin*cos)
= (sin2 - cos2)/(sin*cos)
= sin2/(sin*cos) - cos2/(sin*cos)
= sin/cos - cos-sin
= tan - cot
How do you identify if an equation is function or mere relation?
you will know if it is Function because if you see unlike abscissa in an equation or ordered pair, and you will determine if it is a mere relation because the the equation or ordered pairs has the same abscissa.
example of function: {(-1.5) (0,5) (1,5) (2,5)} you will see all the ordinates are the same but the abscissa are obviously unlike
example of mere relation: {(3,2) (3,3) (3,4) (3,5)} you will see that the ordinates aren't the same but the abscissa are obviously the same. Try to graph it.!
It is a system of counting in 60s. Very common in Babylonian times, it survives in our current measurement of time and of angles. An hour or degree are divided into 60 minutes and each of these is divided into 60 seconds.
tan-1(40/30) = 53.13°
Therefore, the sun is at a 53.13° angle of elevation.
There are several cases when you would want to use the law of sines. When you have angle angle side, angle side angle, or angle side side you would use the law of sines.
This describes a right triangle. This triangle has a base (X ) of 3 ft, a opposite side ( Y) of 9 ft. So, you are looking for the hypothenuse. Use the Pythagoreum theory.
In this case. Your ladder length is called H.
H^2 = X^2 + Y^2
H = sqrt X^2 + Y^2
What are the objectives of teaching trignometry?
The obvious answer is to impart a sound knowledge of the subject in the students. However, you probably want to know why anyone wants to learn trigonometry. The answer to that is this.
Trigonometry is a mathematical tool which is almost essential to know if you want to understand how to build structures cheaply and effectively. With trig. it's easy to figure out where things are most likely to break and how thick structural parts must be to carry loads safely. Trig. is also very useful to understand waves - all sorts of waves such as radio waves and waves on water.
Without trig. engineers would waste so much time trying to work things out that they'd never succeed in any job.
What are rigid rectilinear figures?
The only rectilinear figure is a triangle, or one composed of several triangles joined together.
A guy wire attached to a tower 181 feet from the base (190 - 9) and making an angle of 21 degrees with respect to the ground is 505 feet long.
sin (21) = 181 / x
x = 181 / sin (21)
Note: An angle of 21 degrees with respect to the ground is unrealistic. It is probably more correct to say 21 degrees with respect to the tower, which is 69 degrees with respect to the ground. In this case, the guy wire is 194 feet long.
What are the six trigonometric functions of 180 degrees?
sin(180) = 0
cos(180) = -1
tan(180) = 0
cosec(180) is not defined
sec(180) = -1
cot(180) is not defined.
its short for sine. theres sine, cosine, and tangent. sine is opposite over adjacent for the sides of a triangle (or angles)
Can you transform sine functions into cosine functions?
If you know the measure of one angle, and the length of one side of a triangle, you can find the measures of the other sides and angles. From there, you can find the values of the other trig functions.
cos (x) = sin (90-x) in degrees
there are other identities such as cos^2+sin^2=1, so cos^2=1-sin^2
Pancakes, because astronauts only kayak with pineapples.
Find the cot of a 50 degree angle?
the cotangent of a 50 degree angle is -3.678
This is in Radians.
The cotangent of a 50 degree angle is .8391 (rounded) degrees.
Cos of 850 degrees?
850 deg = 130 + 360*2 = 130 deg
By the graph of the cosine: cos(130) = -cos(50)
and cos(50) is not a fraction of a root.
cos(50) = 0.6427876...
Therefore, cos(850) = -0.6427876...
Use the Pythagorean Theorem: a^2 + b^2 = c^2 where c is the longest side (hypotenuse) of the right triangle.
So
a = 12
b = 12
(12)^2 + (12)^2 = c^2
144 + 144 = c^2
288 = c^2
*Take the square root of both sides
sqrt(288) = c
16.97056... = c
After rounding to the nearest foot, you find that c ~= 17ft
What trigonometric value is equal to cos 62?
The solution is found by applying the definition of complementary trig functions:
Cos (&Theta) = sin (90°-&Theta)
cos (62°) = sin (90°-62°)
Therefore the solution is sin 28°.
What is the angular velocity in radians per second of the second hand of a clock?
The angular velocity of the second hand of a clock is pi/30 radians per second.
The angular velocity of a wheel taking 45 seconds to rotate once is 2 2/3 pi radians per minute. The diameter of the wheel does not matter in this case.
