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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 an equation that uses spherical trigonometry without a calculator?
Before calculators, trig functions in general were evaluated using a slide rule (fast, but accurate to only 2-3 significant digits, and interpolation tables, which required interpolating between values in a printed table of function values to get up to 3-4 significant digits. Tricks were a big part of the repertoire - for example for small angles of less than about 7 degrees, sin and tangent are equal to the angle in radians. Spherical geometry was fairly labor intensive, to say the least, since several trig functions are used for even simple distance and angle calculations. Special tables were printed for common cases, such as plotting great circle distances and bearings for terrestrial navigation. In a desert island setting, given infinite time and desire, trig functions can be calculated using various converging series, with the Taylor series being a commonly taught (though slow!) example.
Why can tangent values be greater than 1 but sine and cosine values cannot be greater than 1?
Sine and cosine cannot be greater than 1 because they are the Y and X values of a point on the unit circle. Tangent, on the other hand, is sine over cosine, so its domain is (-infinity,+infinity), with an asymptote occurring every odd pi/2.
How do you find amplitude in trigonometry?
The amplitude of a sine (or cosine) curve is the difference between the maximum and minimum values of the curve, measured over a whole cycle.
Why are similar triangles the basis for trigonometry?
That's the definition of trigonometry. Triangles are completely dependent upon their side lengths, and can be defined by only three values.
11 Derive the Newton's forward interpolation formula?
Newton's forward interpolation formula is derived by constructing a series of finite divided differences based on the given data points, then expressing the interpolation polynomial using these differences. By determining the first divided difference as the increments of function values, and subsequent divided differences as the increments of the previous differences, the formula is formulated algebraically as a series of terms involving these differences. This results in a polynomial that can be used to interpolate values within the given data range using forward differences.
How does interpolation fuction to affect the appearance of an image?
Interpolation in image processing affects the appearance of an image by filling in missing pixel values when resizing an image. Different interpolation methods, such as nearest neighbor, bilinear, or bicubic, determine how these missing values are calculated. The choice of interpolation method can impact the sharpness, smoothness, and quality of the resized image.
Finding values of polynomial functions?
Substitute that value of the variable and evaluate the polynomial.
Are a polynomial's factors the values at which the graph of a polynomial meets the x-axis?
false
What does it mean to solve a polynomial?
Find values of the variable for which the value of the polynomial is zero.
How can I use scipy.interpolate.griddata to perform interpolation on gridded data?
To use scipy.interpolate.griddata for interpolation on gridded data, you need to provide the grid points and corresponding values, along with the points where you want to interpolate. The function will then estimate the values at those points using interpolation techniques such as nearest neighbor, linear, or cubic.
The process of estimating values between measured data points is called?
Interpolation.
What is to use a given data to estimate a value between known values?
interpolation
What is estamating a value between two known values in a data called?
Interpolation
What is meant by Piecewise linear interpolation?
Interpolation in general is a way to determine intermediate values from a set of coordinates. Linear interpolation would be to fit a single linear function to the entire set of coordinates. Piecewise linear interpolation would then be to determine intermediate values from the set of coordinates by fitting linear functions between each set of coordinates. Connect-the-dots so to speak.
What are the values at which the graph of a polynomial crosses the x-axis?
The graph of a polynomial in X crosses the X-axis at x-intercepts known as the roots of the polynomial, the values of x that solve the equation.(polynomial in X) = 0 or otherwise y=0
What is the difference between interpolation and extrapolation?
Both, interpolation and extrapolation are used to predict, or estimate, the value of one variable when the value (or values) of other variable (or variables) is known. This is done by extending evaluating the underlying function. For interpolation, the point in question is within the domain of the observed values (there are observations for greater and for smaller values of the variables) wheres for extrapolation the point in question is outside the domain.
