Trigonometry 1
sin(23pi/6)
-1/2
Solve for x: 2cos(x) + 1 = 0 for x between [0, 2pi]
2pi/3, 4pi/3
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Live
x = t + 1
y = t2 +3t
y = x2 + x - 2
Find the conjugate of z = 4-5i
4+5i
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Thomas Jefferson
If sin(x)=3/5 and cos(y)=5/13, then what is tan(x-y)?
33/16
Find the Cartesian equation of the locus of points which are equidistant from the points (0, 3) and (1, -2).
y = (x+2)/5
Daily Double!
x = 2 + cos(2t)
y = 1 - 2sin(2t)
(2+i) / (3-2i)
1/13 (4+7i)
Asymptotes of the equation y=cosec(3x) between [0, 2pi]
x = 0, x = pi/3, x = 2pi/3, x = pi, x = 4pi/3, x = 5pi/3, x = 2pi
If x is between [pi/2, pi] and sin(x) = 3/5, then what is the value of cot(x)?
-4/3
Wild Card! Modulus
Solve for x: x2 + 5|x| - 6 = 0
x = -6, -1, 1, 6
A curve has parametric equations x = t - 1 and y = 2t2 - 1, where 0<t<2.
What is the range of the curve?
y E (-1, 7)
Convert to polar form: z = -4 + 4sqrt(3)i
z = 8cis(2pi/3)
If sin(2A) = m and cos(A) = n, then what is tan(A) equal to?
m / 2n2
Daily Double!
cos-1(cos(4pi/3))
2pi/3
Random: Which team won the 2023 NBA Championship?
Denver Nuggets
Double Points!
There are two balls thrown in the air with positions:
Ball 1: x = 10t and y = 20t - 5t2
Ball 2: x = 60 - 10t and y - 20t -5t2
Find the point(s) of intersection of the two paths, and do the balls collide (with justification)?(30, 15)
Yes, both are there at t = 3
Find the Cartesian equation of the subset: |z - (2 + i)| = 4
(x-2)2 + (y-1)2 = 16
What is the domain and range of the equation:
y = - 2 cos-1(-x-1)
domain: [-2, 0]
range: [-2pi, 0]
Solve for x E [0, pi]:
sin(2x) - sin(x) = 0
x = 0, pi/3, pi
A point P(x, y) moves so that its distance from the point K(-2, 5) is twice its distance from the line x = 1. Find its locus.
(x-2)2/4 - (y-5)2/12 = 1
x = cos(t)
y = 3 sin2(t) - 2
y = -3x2 + 1
Daily Double! Solve for x: x3 - 3x2 + 7x - 5 = 0
x = 1, x = 1+-2i