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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 the relationships between inverse functions?
The inverse of the inverse is the original function, so that the product of the two functions is equivalent to the identity function on the appropriate domain.
The domain of a function is the range of the inverse function.
The range of a function is the domain of the inverse function.
How do you put this into a formula needs times faith equals motivation plus action equals results?
it can be written as follows
nf=m+a=R
Where n stands for needs, f for faith,m for motivation, a for action and R represents result.
What are the values of theta of which secant theta is undefined?
Since secant theta is the same as 1 / cosine theta, the answer is any values for which cosine theta is zero, for example, pi/2.
How do you solve sin2a - sin4a equals cos2a - cos4a?
Probably you should start by looking up the double-angle formulas, reducing the "4a" to some combination of "2a".
What is depression in trigonometry?
The angle of depression is looking downwards to an object from the horizontal
What is the difference between negative sine and cosine graphs and positive sine and cosine graphs?
The negative sine graph and the positive sine graph have opposite signs: when one is negative, the other is positive - by exactly the same amount. The sine function is said to be an odd function.
The two graphs for cosine are the same. The cosine function is said to be even.
What is the angular speed of the minute hand in radian per second?
Angular speed = 2*pi radians per 60 seconds = pi/30 radians per second.
How do you find sin cos and tan?
sine(sin) = opp/hypcosecant(q) = hyp/oppcosine(cos) = adj/hypsecant(q) = hyp/adjtangent(tan) = opp/adjcotangent(q) = adj/opp
What is the third square root of 0.125?
It is not clearly mentioned that whether it is the "THIRD" root we have to calculate.. or the "SQUARE ROOT THREE TIMES.. i.e the EIGHTth ROOT".. The answer posted here before was not correct in a sense that the if the question demands "third square root" which can also mean the "EIGHTth" root..
Re-edit:
It seems rather obvious that this answerer is new to wiki answers and is not in the habit of question interpretation. The question is most likely thus; " What is the cubic root of 0.125. The answer then would be...,
cubic root(0.125)
= 0.5
====( calculate the square root three times?!? sounds like a stretched interpretation )
Do you know what square root means? -_- if u know.. then u clearly know what "third square root means" .. huh -_-
6 trigonometric values of 315 degrees?
To find exact values, you should use the unit circle.
It is good practice, too, to use radians as this is much more helpful in higher levels of math, so, do yourself a favor and learn how to convert degrees into radians and start thinking about the circle in radians instead of degrees.
315 degrees = (7 [Pi])/4 radians
You can use the following conversion to find this: 90 degrees = Pi / 2 radians.
315 / 90 = x / (Pi / 2), solve for x.
Although you can find decimal approximations using a calculator, it is better to find these on the unit circle and start building your knowledge about radians and how they related to each other and the circle. You will soon find out that most of the time you are dealing with a 3, 4, 5 or right triangle.
Turns out that here we are looking at the right triangle in the 4th quadrant of the unit circle. All angles in the 4th quadrant share certain principles. x is positive and y is negative in the 4th quadrant. This means that cos is going to be positive and sin and tan are going to be negative. All right triangles also have similar properties, their sin and cos are going to be equal or differ only by their sign and will be either Sqrt(2)/2 or -Sqrt(2)/2.
Building this intuitive knowledge about the unit circle and the angles it contains will serve you much better than getting decimal approximations.
sin( (7 [Pi])/4 ) = -1/Sqrt(2) = -Sqrt(2)/2
cos( (7 [Pi])/4 ) = 1/Sqrt(2) = Sqrt(2)/2
To find tangent, you need to do a little arithmetic. We know that tan(x) = sin(x) / cos(x), so,
tan( (7 [Pi])/4 ) = sin( (7 [Pi])/4 ) / cos( (7 [Pi])/4 ) = (-Sqrt(2)/2)/(Sqrt(2)/2) = -1
You can also remember that this is a right triangle and tangent is also going to be 1 or -1 depending on the quadrant.
The cossec, sec and cot values are the reciprocals of these values:
cossec( (7 [Pi])/4 ) = 1/sin( (7 [Pi])/4 ) = 1/(-Sqrt(2)/2) = -Sqrt(2)
sec( (7 [Pi])/4 ) = 1/cos( (7 [Pi])/4 ) = 1/(Sqrt(2)/2) = Sqrt(2)
cot( (7 [Pi])/4 ) = 1/tan( (7 [Pi])/4 ) = cos( (7 [Pi])/4 ) / sin( (7 [Pi])/4 ) = -1
Definition of complement of a set?
S', the complement of a set S, in the context of the universal set U, is the set of all elements of U that are not in S.
It is important to note that a complement is defined only in terms of the universal set. The following, rather crude example illustrates the point. Suppose S is the set of all boys.
Then S' may be the set of all girls if U = youngsters;
or S' = set of all girls, women and men if U = people;
or S' = set of all girls, women, men, dogs, cats, cows, ... if U = mammals; and so on.
As you see, changing U alters S'.
The cosine of 0.57 degrees is 0.999951. The cosine of 0.57 radians is 0.841901
