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The unit circle chart also involves sin, cos, tan, sec, csc, cot. Fortunately, you don’t have to memorize everything involved in the entire unit circle. All you need to do is apply the basic concepts you know about the circle and about right triangles.
Cotangent. 𝑓𝑓(𝑥𝑥) = cot(𝑥𝑥) = 1 tan(𝑥𝑥) = cos(𝑥𝑥) sin(𝑥𝑥) Domain: (−∞,∞) except for 𝑥𝑥= ±𝑛𝑛 𝜋𝜋 Range: (−∞,∞) Odd/Even: Odd. Period: 𝜋𝜋. Asymptotes at 𝑥𝑥= ±𝑛𝑛 𝜋𝜋 General Form: 𝑓𝑓(𝑥𝑥) = 𝑎𝑎sin[𝑏𝑏(𝑥𝑥−ℎ)] + 𝑘𝑘 *This ...
tan(𝑥)) cot( )=cos(𝑥) sin(𝑥) sec( )= 1 cos(𝑥) csc( = 1 sin(𝑥) Pythagorean Identities (cos 2 )+sin( )=1 2sec( )−tan2( )=1 2csc( )−cot2( )=1 Double Angle Identities (sin2 )=2sin( )cos( ) (cos2 )=1−2sin2( ) (cos2 )=2cos2( )−1 cos(2 )=cos2( )−sin2( ) tan(2 )=2tan(𝑥) 1−tan2(𝑥) Sum Difference Identities
The general forms of the equations for sine, cosine, cosecant, and secant: • Sine: y = d + a sin (bx – c) • Cosine: y = d + a cos (bx – c) • Tangent: y = d + a tan (bx – c) • Cosecant: y = d + a csc (bx – c) • Secant: y = d + a sec (bx – c) • Cotangent: y = d + a cot (bx – c) The constants a, b, c, and d, in each ...
Take the reciprocal of each value and plot the ordered pair in the coordinate plane. This lesson shows how to graph the reciprocal trigonometric functions (y = csc x, y = sec x and y = cot x) using the y = sin x, y = cos x and y = tan x functions.
sec. y. tan θ = cot θ = y. Facts and Properties. Domain. The domain is all the values of θ that can be plugged into the function. sinθ , θ can be any angle cosθ , θ can be any angle. 1 tanθ , ⎛ θ ≠ ⎜ n + ⎞ ⎟ π , n = 0, ± 1, ± 2, ... ⎝ 2 ⎠ cscθ , θ ≠ n π = ± ± , n 0, 1, 2, ... secθ θ ≠ ⎛ 1 ⎞ , ⎜ ⎝ n + ⎟ π , n = 0, ± 1, ± 2, ... 2 ⎠.
We learn why graphs of tan, cot, sec and cosec have a periodic gap in them (also known as a discontinuity). We learn how to sketch the graphs.
