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How is tangent defined?
The tangent of an angle theta is defined as sine(theta) divided by cosine(theta). Since the sine and cosine are Y and X on the unit circle, then tangent(theta) is Y divided by X. The tangent of a function at a point is the line going through that point which has slope equal to the first deriviative of the function at that point.
What is the definition of a tangent function?
Tangent (theta) is defined as sine (theta) divided by cosine (theta). In a right triangle, it is also defined as opposite (Y) divided by adjacent (X).
What is the answer to y equals 4x-5 in a mapping diagram?
9
What is tangent to the x axis?
Well, since a tangent line touches a line in one spot, the Y axis could be considered tangent to the X axis.
What is 1 divided by x divided by 2 divided by y?
0.5
What is a number divided by a minus number?
X divided by -Y is the same as -X divided by Y. Or - (X/Y)
How do you determine the height of a mast?
You can determine the height of a mast by using the tangent. Measure the distance from the base, and the angle of elevation of the top of the mast as observed from that distance. The tangent is y over x, so substitute x for the distance from the base and y for the height of the mast. Solve from there. For instance, if the angle is 60 degrees and the x distance is 25 feet, then... tan (60) = y / 25 25 tan (60) = y y = 43.3
Find the equation of the line tangent to the graph of y equals cos2x at x equals pi divided by 4?
0.5
What are the sum and difference identities for the sine cosine and tangent functions?
Sine sum identity: sin (x + y) = (sin x)(cos y) + (cos x)(sin y)Sine difference identity: sin (x - y) = (sin x)(cos y) - (cos x)(sin y)Cosine sum identity: cos (x + y) = (cos x)(cos y) - (sin x)(sin y)Cosine difference identity: cos (x - y) = (cos x)(cos y) + (sin x)(sin y)Tangent sum identity: tan (x + y) = [(tan x) + (tan y)]/[1 - (tan x)(tan y)]Tangent difference identity: tan (x - y) = [(tan x) - (tan y)]/[1 + (tan x)(tan y)]
What are the tangent line equations of the circle x2 plus y2 -6x plus 4y plus 5 equals 0 when the circle passes through the x axis?
Equation of circle: x^2 +y^2 -6x +4y +5 = 0 Completing the squares: (x-3)^2 +(y+2)^2 = 8 Radius of circle: square root of 8 Center of circle: (3, -2) Circle makes contact with the x axis at: (1, 0) and (5, 0) Slope of 1st tangent: 1 Slope of 2nd tangent: -1 1st tangent line equation: y = 1(x-1) => y = x-1 2nd tangent line equation: y = -1(x-5) => y = -x+5
What is a tangent ratio?
The tangent is the ratio of sine over cosine; also, in a unit circle, Y over X.
Why does the tangent increase as the angle increases?
The tangent of an angle in a right triangle is defined as the ratio of the length of the opposite side to the length of the adjacent side. As the angle increases, the length of the opposite side grows faster than the adjacent side decreases, leading to a larger ratio. Additionally, on the unit circle, the tangent function corresponds to the y-coordinate (sine) divided by the x-coordinate (cosine), and as the angle approaches 90 degrees, the cosine approaches zero, causing the tangent to increase towards infinity. Thus, the tangent function is increasing for angles between 0 and 90 degrees.
