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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 are the values of theta of which co secant theta is undefined?
Any value for which sin(theta) = 0, i.e. theta = N*180, N being an Integer.
Why is degrees not taken as the angle of reference in trignometry?
They often are. Sometimes, however, radians are used for the measures of angles and for labeling graphs. This is because later aspects of trigonometry, like polar coordinates, arc lengths, and wave graphs, are more easily explored with radians. Pi commonly appears and is more easily understood as π than as 3.14159.... Circles, with areas of πr^2, are frequent and periods of wave function are almost always expressed in radians. Radians become as useful and widespread as degrees.
How do you remember sin and cos values?
Mnemonics
A common use of mnemonics is to remember facts and relationships in trigonometry. For example, the sine, cosine, and tangent ratios in a right triangle can be remembered by representing them as strings of letters. For instance, a mnemonic for English speakers is SOH-CAH-TOA:Sine = Opposite ÷ HypotenuseCosine = Adjacent ÷ HypotenuseTangent = Opposite ÷ Adjacent
One way to remember the letters is to sound them out phonetically (i.e. "SOH-CAH-TOA", which is pronounced 'so-kə-tow'-uh').Another method is to expand the letters into a sentence, such as "Some Old Hippy Caught Another Hippy Trippin' On Acid". or "Some Old Houses, Can't Always Hide, Their Old Age"
What are the angles of a rhombus with an area of 40 square centimeters and sides of 15 centimeters?
Suppose the rhombus is ABCD.
Consider the triangle ABC, whose area will be 40/2 = 20 sq cm.That is, 0.5*AB*BC*sin(B) = 20
sin(B) = 40/225 = 0.1777... recurring.
Therefore B = arcsin(1.777...) = 0.1787 or 2.9629 radians or equivalently, 10.24 or 169.76 degrees.
What is a polar triangle in spherical trigonometry?
for any spherical triangle on any sphere there associated another triangle called the polar triangle associated with this spherical triangle with the property that the sum of any angle (or side) of one of these two triangles and the length of the side (and the angle)of the other triangle is alway equil to 180 degrees
Compass Calibration
The Automatic Compass Calibration feature eliminates
the need for the operator intervention under normal
conditions. If the CAL indicator is lit, the compass needs
to be calibrated. A good calibration requires a level
surface and an environment free of large metal objects
such as large buildings, bridges, underground cables,
railroad tracks, etc.
Manual Compass Calibration
Compass calibration can also be requested. To manually
calibrate the compass, use the STEP button to step to the
compass/ temperature display and then hold down both
the STEP and US/M buttons simultaneously until the
CAL symbol is displayed. Release the buttons once the
CAL symbol appears. Manual compass calibration has
been initiated at this point. Drive the vehicle in circles in
an area free from large metal objects until the CAL
symbol is extinguished.
When the CAL indicator goes off, the compass is calibrated
and should display correct headings. Verify
proper calibration by checking North (N), South (S), East
(E), and West (W). If the compass does not appear
accurate, repeat the calibration procedure in another area.
Compass Variance
Variance is the difference between magnetic North and
geographic North. For proper compass function, the
correct variance zone must be set.
Setting the Compass Variance
Refer to the variance map for the correct compass variance
zone. To check the variance zone, the ignition must
be on and the compass / temperature displayed. Hold
down both the US / M and STEP buttons simultaneously
until the VAR symbol is lit and then immediately release
both buttons. The current variance zone will now be
displayed. To change the zone, press the STEP button
until the correct zone is displayed. Wait for about 5
seconds. The trip computer will store this variance in
memory and the compass will resume normal operation.
Where is trigonometric function in negative?
In the domain [0, 2*pi],sin is negative for pi < x < 2*pi
cos is negative pi/2 < x < 3*pi/2 and
tan is negative for pi/2 < x < pi and 3*pi/2 < x < pi.
Also, the same applies for all intervals obtained by adding any integer multiple of 2*pi to the bounds.
Does an angle of 1 radian stay the same if the size of the circle changes?
Yes. Angles remain the same irrespective of scale.
What is a conclusion based on evidence?
A conclusion based on evidence is called, well, a conclusion.
It could also be a deduction or a syllogism, but that is unnecessarily high-falutin, so to speak.
What is the different shape a relation from a function?
When graphed, a function has any shape so that all vertical lines will cross the graph in at most one point. A relation does not have this condition. One or more vertical lines may (not must) pass thru a relation in more points.
15 degrees of travel equal to how many hours?
The time taken will depend on the speed at which the journey is undertaken.
What is the relevance of the number 1.414 to a 45 degree angle?
The number 1.414... (square root of 2) is two times the cosine or sine of a 45 degree angle.
The reason for this is that for a 45 degree angle, the two sides are cosine and sine, they are equal, and if you solve using the Pythagorean theorem with a hypotenuse of 1, the two sides are each (21/2)/2.
How to find the chord length of a curve with radius and 2 bearings given?
Suppose the radius is r and the bearings of the two points, P and Q are p and q respectively.
Then
the coordinates of P are [r*cos(p), r*sin(p)] and
the coordinates of Q are [r*cos(q), r*sin(q)].
The distance between these two points can be found, using Pythagoras:
d2 = (xq - xp)2 + (yq - yp)2
where xp is the x-coordinate of P, etc.
You could start by spelling out the words properly so that we can read your question rather than having to decipher it.
What are practical applications of trigonometry?
To name a few, the practical applications are:
1. Acoustics
2. Architecture
3. Astronomy ( and Navigation)
4. Cartography
5. Chemistry
6. Civil Engineering
7. Computer Graphics
8. Crystallography
9. Geophysics
10. Economics (Analysis of Financial Markets)
11. medical imagining
12. Seismology
13. Phonetics
14. Probability and Statistics. and etc.
How do you verify the identity of cos θ tan θ equals sin θ?
To show that (cos tan = sin) ???
Remember that tan = (sin/cos)
When you substitute it for tan, cos tan = cos (sin/cos) = sin
QED
