Sin/Cos/Tan
If the sinϴ = 2/3. What is the csc
3/2
The opposite side of a 45* angle is 3. What are the lengths of the other two sides?
Adjacent: 3
Hypotenuse: 3√ 2
What is 211º in radians?
3.68
Write the equation for a parabola that has a focus of (-3, 1), and a directrix of 0.
(1/2)x2 + 3x + 5 = y
What is the law of Sines?
a/Sin(A)=b/Sin(B)= c/Sin(C)
If the cos(ϴ)=4/5, what is the tan(ϴ)
3/4
The opposite side of a 60* angle is 5√ 3. What are the lengths of the other two sides?
Hypotenuse: 10
What is 1.87 radians in degrees?
107.14*
Write an equation for an ellipse with the foci at (0, 6) and (0, -6), and vertices at (4, 0) and (-4, 0)
x2 / 16 + y2 / 52 = 1
What is the law of Cosines?
a2 = b2 + c2 – 2bcCos(A)
What is the tan of a 45 degree angle in a 45-45-90 triangle?
1
The hypotenuse of a 45-45-90 triangle is 13 cm long. What is the length of the other two sides?
Both sides are each 13/√ 2cm
If a circle has a diameter of 10cm. What is length of the circumference in cm?
10π cm
or
31.42 cm
Use the focus and directrix to find the equation of a parabola that has a focus of (4, 7), and a directrix of 3.
(1/8)x2 - x + 7 = y
(x-h)2/a2 - (y-k)2/b2 =1
is the formula for what function?
Hyperbola
What is the cos(x), if the sin(x) = 2 / 5 ?
√(21)/5
What is the cos of the 60* angle of a 30-60-90 triangle?
√(3)/2
A circle has an arc of 3.03, and a radius of 6. What is the measure of the angle that intercepts the arc?
28.93
Write an equation for a hyperbola that has foci at (5, 0) and (-5, 0), and vertices at (4, 0) and (-4, 0)
x2 / 16 - y2 / 9 = 1
What special triangle has side lengths that measure 1,2, √ 3 ?
30-60-90 triangle
What is the tan(x), if the cos(x) = 7 / 15? Round to the nearest hundreth.
1.90
The hypotenuse of a 30-60-90 triangle is 50 m. What are the length other two sides?
Short side: 25 m
Long side: 25√ 3 m
Complete the square of this circle to discover it's center and radius:
x2 + y2 - 10x - 16y + 17 = 0
x2- 10x + 25 + y2 - 16y + 64 = -17 +25 + 64
(x-5)2 + (y-4)2 = 72
Midpoint (5,4)
Radius √ 72
Write the equation for a hyperbola that has the foci at (0, 11) and (0, -11) and the vertices at (0,6) and (0,-6)
y2 / 36 - x2 / 85 = 1
Write an equation for an ellipse that has foci at (0, 10) and (0, -10), and vertices at (8, 0) and (-8, 0).
x2 / 64 + y2 / 164 = 1