Unit 4: Trig Identities
Name one of the identities for
cos(2theta)
cos^2theta-sin^2theta
2cos^2theta-1
1-2sin^2theta
How would you evaluate the following log using change of base?
log_12 36
log36/log12
What are the dimensions of the following matrix?
[[1, 3, 4], [2, 7, -1]]
2xx3
Given the coordinate (2, (3pi)/4) , find another polar coordinate 0<theta<2pi to represent the same point.
(-2, (7pi)/4)
Identify the type of conic.
2x^2+2y^2-28x-16y-100=0
Circle
What is the tangent double angle identity?
tan(2theta)=
(2tantheta)/(1-tan^2theta)
Condense the following expression into one logarithm.
12log_8a-4log_8b
log_8(a^12/b^4)
Find the determinant of the matrix.
[[-4, 3], [4, -5]]
8
Classify the polar curve (be specific!)
r=3cos(3theta)
3-Petal Rose
Write the equation of a circle with the center at (2, -1) and a circumference of 14pi
(x-2)^2+(y+1)^2=49
Find the exact value of
2sin(pi/8)cos(pi/8)
sqrt2/2
Expand the following logarithm.
ln(x^4y)^6
24lnx+6lny
Multiply the matrices
[[-4, -3],[-1, -1]]cdot[[6], [-2]]
[[-18], [-4]]
Convert the coordinate (-1, sqrt3) into polar form with r>0 and 0leqtheta<2pi
(2, (2pi)/3)
Determine the eccentricity of the hyperbola.
(x+2)^2/100-(y-6)^2/64=1
sqrt41/5
text(Given the following information, find) tan(2theta)
cos theta=-4/5 and sin theta>0
-24/7
Solve the exponential equation.
64^(2-3x)=1/16
8/9
Find the inverse of the matrix.
[[2, -9], [-1, 6]]
[[2, 3], [1/3, 2/3]]
Convert the complex number (5sqrt3)/2i+5/2 into polar form
5(cos (pi/6)+isin(pi/6))
Find the foci for the ellipse
(x-2)^2/25+(y+2)^2/9=1
(6, -2), (-2, -2)
Solve the equation for 0leqx<2pi
cos^2x=2+2sinx
(3pi)/2
Solve the following log equation.
log_6(x+1)+log_6x=1
2
Find the determinant of the matrix
[[3, -3, -3], [-5, -1, 0], [4, -1, 0]]
-27
Convert the polar equation r=6costheta+2sintheta into rectangular form.
(x-3)^2+(y-1)^2=10
Rewrite the following conic equation into standard form.
9x^2-y^2-54x-16y-127=0
(x-3)^2/16-(y+8)^2/144=1