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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
Is Subtraction is associative?
True. You may not be able to switch numbers like 4-2=2-4 but you would say 4-2=-2+4
* * * * *
That is not the associative property!
The associative property requires that the order of operation can be changed without affecting the final result. This is clearly not the case with subtraction since:
(5 - 3) - 2 = 2 - 2 = 0
while
5 - (3 - 2) = 5 - 1 = 4
Each angle may be used as a 'reference angle'. A 30 deg. angle in QI will have a sides, x = (sq rt 3)/2 , y= 1/2, r = 1. An angle of 150 deg (180 - 30) will create a triangle in Q2 with the same lengths except x is now negative. So if you know all trig values for 30, then change the signs for cos and tan because x is now negative and you know the values of all. Similarly for 210 deg (180+30) creates the same triangle in Q3 but both x and y values are neg. Sin and cos are neg, but tan (divide 2 neg's) is positive. In Q4 (360 - 30) creates a 330 deg angle for a triangle that is the same shape, but y is neg and x is pos so that sin and tan are neg but cos is pos.
ex: sin 30 = 1/2 (Q1), sin 150 = -1/2 (Q2), sin 210 = -1/2 (Q3), sin 330 = 1/2 (Q4)
notice only the sign (+/-) changes.
Most trig classes teach you that Q1 all trig functions are pos, Q2 sin is pos, Q3 tan is pos, Q4 cos is pos. Remember this and the 1st Quadrant values and then you can get all trig functions using the concept of a reference angle.
What has one pair of parallel sides of different lengths and two right angles?
Right angled trapezium
Can you give us uses of Trigonometry in real life?
Figuring out distances, diameters of large objects, and more. Trig is also used in careers.
Can you make a plot for equals 4 sec to the second power time 2x?
Yes, but it will depend on the domain.
Since sec(x) = 1/cos(x), you may find it easier to work with
y = 4/cos2(2x)
The graph will be a set of U shapes. At even multiples of pi radians (180 degrees), the U-shapes will have their minima ( = 4). At odd multiples of pi radians they will be asymptotically +infinity.
What is the graph of tangent functio is periodic at?
The graph of the tangent function is periodic at every point. Periodic means that the value of the function at every point is repeated after an integer multiple of the period.
How do you name a triangle by the angle measure?
If it has one right angle (90 degrees), it is a right triangle.
If it has one obtuse angle (more than 90 degrees), it is an obtuse triangle.
If it has more than one acute angle (less than 90 degrees), it is an acute triangle.
Parts of the cartesian coordinate system?
It has a horizontal number line called the x axis
It has a vertical number line called the y axis
Both axes are perpendicular to each other and meet at the origin
Graphs can be plotted on it
What are real life angles with degrees geometry?
look at an analog clock and whatever time it is you can determine if it is a right angle, acute, obtuse, or straight. look at the borders of doors or the ceiling
it is used in real life situation to fin the height of thing and in math you use it to find the length of one of the sides.
The equation x2 + y2 = 1 is the equation for the unit circle, with center at (0,0). The intersections between that circle and the lines emmanating from (0,0) having angles of 30, 45, 60, 75, and 90 degrees relative to the positive x-axis would be 30 = (0.866, 0.5), 45 = (0.707, 0.707), 60 = (0.5, 0.866), 75 = (0.259, 0.966), and 90 = (1, 0).
In each case, the x coordinate is the cosine of the angle and the y coordinate is the sine of the angle. All answers have been rounded to three significant places.
Since x is a constant (2.8) the only variable changing would be y, that means that it is a vertical line that crosses the x-axis in 2.8
If you also know its shadow then you can work out the angle of elevation
What is the distance between A7 0 and b2 -5?
Dist2 = [7 - 2]2 + [0 - (-5)]2 = 52 + 52 = 2*52
So Dist = 5*sqrt(2) = 7.0711
What is the Daily average for 4155.88 million of instructions per second?
It is approx 359 trillion per day.
In what products do gas tubes find application?
Product types included diodes, rectifiers, control-type industrial triodes, hydrogen and nonhydrogenthyratons, and other gas and vapor tubes.
How do you write a differential equation?
You take algebra, and trigonometry, and calculus, and then differential equations, and then you just do it. Until you've taken those classes, no explanation I could give would do you much good; after you've taken them, you won't need it.
What is the equivalent value of versine A?
versine(A) = 2*sin^2(A/2) = 1 - cos(A)
The following is an attempt to describe versine. It is much easier to follow the description if you sketch it.
In a circle with radius = 1 consider a radius inclined at A degrees to the horizontal.
If the radius meets the circumference at P(x, y) then x = cos(A) and y=sin(A).
Then versine A is the distance from the point, on the x-axis, below P to the point where the circle meets the x-axis.
What is the discriminant of y6x squire x-1?
y = 6x2 + x -1 ??
discriminant = b2 - 4ac = 12 - 4(6)(-1) = 25
What are trigonometric functions in mathematics?
The basic ones are:
sine, cosine, tangent, cosecant, secant, cotangent;
Less common ones are:
arcsine, arccosine, arctangent, arccosecant, arcsecant, arccotangent;
hyperbolic sine, hyperbolic cosine, hyperbolic tangent, hyperbolic cosecant, hyperbolic secant, hyperbolic cotangent;
hyperbolic arcsine, hyperbolic arccosine, hyperbolic arctangent, hyperbolic arccosecant, hyperbolic arcsecant, hyperbolic arccotangent.
Using Pythagoras' theorem 3rd side is: 38.98 cm rounded to 4 s.f.
Using trigonometry smallest angle is 44.12 degrees rounded to 4 s.f.
