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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
Which angle length does cosine give you?
Sides have lenght, angles do not.
Cosine is the ratio of the adjacent side to the hypotenuse. Cosine can be used to find either of these sides if the other is known.
You cannot. With only the base given (a parallelogram) you don't even know what the shape is: it could be a parallelepiped, or a parallelogram based pyramid or one of several other shapes.
How do you work out the gradiant on a ramp?
Divide the height of the ramp by the length of the ramp (rise over run).
3*pi/4, 7*pi/4, 11*pi/4 and 15*pi/4 radians or2.3562, 5.4978, 8.6394 and 11.7810 radian (approx).
How do you solve 5x plus 2x plus 5 plus 1 minus x equals 18?
The solution of this equation is the value of variable 'x' for which L.H.S.= R.H.S. The given equation is: 5x+2x+5+1-x=18
6x+6=18
Adding -6 on both sides, we get
6x=12
Dividing both sides by 6, we get
x=2
Solution is x = 2.
Can trigonometry be used with right triangles only?
No, trigonometry can be used with any triangle, right angle or not.
While the primary trigonometric functions are defined in relation to right triangles with hypoteneuse equal to 1, that is just a special case where the function is easier to define. Sine (theta), for instance, is opposite over hypotenuse, where the angle on the other end of adjacent is a right angle. Even if you don't have a right angle, the functions can help you find a superposition of a right triangle on any triangle, and that can help you solve many different kinds of problems.
The laws of sines and cosines, for instance, apply to any triangle.
How do you make height as a function of time?
You record a person's height and age (time) from birth onwards.
Can you solve sinx plus cosx equals 0.5?
Start by squaring both sides of the equation to get,
(sinx + cosx)2 = 0.25
Simplify the left side to get
sin2x + 2sinxcosx + cos2x = 0.25
Using the Pythagorean identity gets
2sinxcosx + 1 = 0.25
2sinxcosx = -0.75
Using the double angle formula gets
Sin(2x) = -0.75
Take the arcsin to get
2x = sin-1(-0.75)
x = sin-1(-0.75)/2
Now, a scientific calculator can be used to find the solutions.
Use the tangent ratio:
250*tan(62.2) = 474.1671924
250*tan(59.5) = 424.4157798
Subtracting one from the other is the height of the tower which is about 50 meters.
You cannot.
How do you demonstrate parallax?
Look at two objects, say one about a foot away, and the other about two feet away. Move your head until the objects appear to be lined up with each other.
Now, cover and uncover one eye. Repeat it a couple of times. Then do the same thing with the other eye.
Depending on which eye is dominant, in one case the two objects will stay lined up, and in the other case they will appear to move with respect to each other.
That is parallax, which is simply the difference in perception between the viewpoints, in this case, the eyes.
Astronomers use parallax to measure long distances in space. They take pictures of an area of space they are interested in, wait 6 months, and take pictures of the same area of space. They compare the pictures. Most far distant stars will appear to be in the same position, so they line up the two pictures based on the far distant stars. Then they notice that some stars appear to be in different positions. They use trigonometry to measure the parallax error between the two pictures. Since they know the distance between the two observation points is about 186 million miles, and they know the angles of both observations, they have enough information to calculate distance to the star.
What is different between 1st angle and 3rd angle?
Basically its just where you position the views of the main object, in first angle projection, if you view the object from the left, the view is drawn to the right of the object, in third angle projection, its drawn on the viewing side.
What does 35 degrees 25' means?
In degrees-minutes notation, 35 degrees 25 minutes (35° 25') represents a specific angle measurement. The 35 degrees signifies the whole number of degrees, while the 25 minutes represents the additional fractional part of a degree. This notation is commonly used in navigation, astronomy, and other fields where precise angle measurements are necessary.
How do you find exact value without calculator?
sine tables, that's how they did it before calculators, there are formulas as well
How do you calculate the sides of a parallelogram given the height and longer diagonal?
The height and longer diagonal do not provide enough information to calculate the sides.
When is sin x equal to cos x times cos x?
To figure this out, graph y = sin x and y = cos2 x on the same piece of paper or graphing utility and find the points where the graphs intersect.
To determine this analytically, take the equation sin x = cos2 x and divide both sides by cos x to obtain the equivalent expression tan x = cos x. What this means is that the ratio of the opposite side of the triangle formed by angle x and the triangle's adjacent side is equal to the ratio of the triangle's adjacent side divided by its hypotenuse. This can be expressed by using the variables x and y to represent the opposite side and the adjacent side, respectively, by the expression
x2/y2 = y2/(x2 + y2)
where x2 + y2 equals the hypotenuse squared and x2/y2 equals the tangent squared. Now you can solve for either y or x by plugging in any number into the other (here we will solve for x by plugging 1 into y to obtain the expression
x2 = 1/(x2 + 1)
This can be rearranged to the form
x4 + x2 - 1 = 0
We can now solve for x2 using the quadratic formula.
[-1 + or - (1 + 4)1/2]/2
This equals negative one plus or minus the square root of five, all divided by two. Since we need to find the square root of x2, and negative numbers don't have real square roots, and negative one minus the square root of five divided by two is negative, we shall take the square root of negative one plus the square root of five divided by two, since this yields a real value. This approximately equals 0.6180. This, divided by our chosen y value, is the tangent of all angles for which the sine equals the cosine squared, and since our chosen y-value is 1, we can simply use a calculator's tan-1 function to find the value within the domain 0 x = 31.7175 + 180n where n is any integer, positive or negative.
