Question 101198
a. sin(t) = 1/2
t = pi/6
t = pi/6 and t = 5*pi/6
{{{graph(700,200,-1,6.3,-3,3,1/2,sin(x))}}}
b. 2*cos^2(theta) - 3*cos(theta) + 1 = 0
2*cos^2(theta) - 2*cos(theta) - cos(theta) + 1 = 0
2*cos(theta)(cos(theta) - 1) - 1(cos(theta) - 1) = 0
(2*cos(theta) - 1)(cos(theta) - 1) = 0
2*cos(theta) - 1 = 0 and cos(theta) - 1 = 0
cos(theta) = 1/2 and cos(theta) = 1
theta = pi/3, 5*pi/3, 0, and 2*pi
{{{graph(700,200,-1,6.3,-1,1,2*cos(x)^2 - 3*cos(x) + 1)}}}
c. simple
d. 2*cos(2t) = 7cos(t)
2*cos(2t) - 7*cos(t) = 0
2( cos(t + t) ) - 7*cos(t) = 0
2( cos(t)^2 - sin(t)^2 ) - 7*cos(t) = 0
2( cos(t)^2 - ( 1 - cos(t)^2 )) - 7*cos(t) = 0
2( 2*cos(t)^2 -  1) - 7*cos(t) = 0
4*cos(t)^2 - 7*cos(t) - 2 = 0
4*cos(t)^2 - 8*cos(t) + cos(t) - 2 = 0
4*cos(t)(cos(t) - 2) + 1(cos(t) - 2) = 0
(4*cos(t) + 1)(cos(t) - 2) = 0
4*cos(t) + 1 = 0 and cos(t) - 2 = 0
cos(t) = -1/4 and cos(t) = 2 ... nonexistant
I do not have a calculator with the inverse process with me ...
{{{graph(700,200,-1,6.3,-2,2,-.25,cos(x),2*cos(2x),7*cos(x))}}}