Because that is the way the tan function is defined!
No, white and tan are not the same colors. The links below show the difference between the colors.
The answer is relatively simple if you know hyperbolic functions. Suppose x is real so that ix is an imaginary number. Then tanh x = -i*tan(ix) So tan(ix) = (tanh x )/-i = i*tanh x = i * sinh x/csh x = i*(ex - e-x)/(ex + e-x) = i*(1 - e-2x)/(1 + e-2x)
6.00
55.000
This is a trigonometric integration using trig identities. S tanX^3 secX dX S tanX^2 secX tanX dX S (secX^2 -1) secX tanX dX u = secX du = secX tanX S ( u^2 - 1) du 1/3secX^3 - secX + C
ln |sec x + tan x| + C
The value of tan and sin is positive so you must search quadrant that tan and sin value is positive. The only quadrant fill that qualification is Quadrant 1.
The third quadrant.
Example: Express sin 120⁰ as a function of an acute angle (an angle between 0⁰ and 90⁰).Solution:Each angle θ whose terminal side lies in quadrant II, III, or IV has associated with it an angle called the reference angle, alpha (alpha is formed by the x-axis and the terminal side).Since 120⁰ lies on the second quadrant, then alpha = 180⁰ - 120⁰ = 60⁰.Since sine is positive in the second quadrant, sin 120⁰ = sin 60⁰.Example: Express tan 320⁰ as a function of an acute angle.Solution:Since 320⁰ lies on the fourth quadrant, then alpha = 360⁰ - 320⁰ = 40⁰.Since tangent is negative in the fourth quadrant, tan 320⁰ = -tan 40⁰.
sinx*secx ( secx= 1/cos ) sinx*(1/cosx) sinx/cosx=tanx tanx=tanx
If tan A = 1/2, then sin A = ? We use the Pythagorean identity 1 + cot2 A = csc2 A to find csc A, and then the reciprocal identity sin A = 1/csc A to find sin A. tan A = 1/2 (since tan A is positive, A is in the first or the third quadrant) cot A = 1/tan A = 1/(1/2) = 2 1 + cot2 A = csc2 A 1 + (2)2 = csc2 A 5 = csc2 A √5 = csc A (when A is in the first quadrant) 1/√5 = sin A √5/5 = sin A If A is in the third quadrant, then sin A = -√5/5.
Cotan(theta) is the reciprocal of the tan(theta). So, cot(theta) = 1/2.
tan theta = sqrt(2)/2 = 1/sqrt(2).
Assuming sin equals 0.3237, the angle is in quadrant I.
d/dx(uv)=u*dv/dx+v*du/dxd/dx(secxtanx)=secx*[d/dx(tanx)]+tanx*[d/dx(secx)]-The derivative of tanx is:d/dx(tan u)=[sec(u)]2*d/dx(u)d/dx(tan x)=[sec(x)]2*d/dx(x)d/dx(tan x)=[sec(x)]2*(1)d/dx(tan x)=(sec(x))2=sec2(x)-The derivative of secx is:d/dx(sec u)=[sec(u)tan(u)]*d/dx(u)d/dx(sec x)=[sec(x)tan(x)]*d/dx(x)d/dx(sec x)=[sec(x)tan(x)]*(1)d/dx(sec x)=sec(x)tan(x)d/dx(secxtanx)=secx*[sec2(x)]+tanx*[sec(x)tan(x)]d/dx(secxtanx)=sec3(x)+sec(x)tan2(x)
There's a mnemonic for this: All Students Take Calculus. Starting in the first quadrant, and moving counterclockwise until the last, give each quadrant the first letter of thos words in order. A represents all 3, s represents sine, t represents tangent, and c represents cosine. If the letter appears in a quadrant, it is positive there. If not, it is negative there.In quadrant 2, only sine is positive.