unit 3 test math
sin(pi)
0
sin(pi/2)
1
Pythagorean Identity
1+tan^2x=sec^2x
sin(pi/6)
1/2
the conventional domain for y=cos(x) is restricted to [0,pi] in order to define y=cos^-1(x) as a function. what intervals could also be the restricted domain of y=cos(x) in order for it to be invertible, making y=cos^-1(x) its inverse function
[-2pi, -pi] [-pi, 0] [pi, 2pi]
not an identity
cos(-x)=-cos(x)
half angle formula
cos(a/2)=+/- sqrt (1+cosa/2)
complementary angle theorem
cos(pi/2-x)=sinx
cos(a-b)
cosAcosB+sinAsinB
cos(a+b)
cosAcosB-sinAsinB
Reciprocal Identity
cotx=1/tanx
(cosa-cosB)^2+(sina-sinB)^2=(cos(a-B)-1)^2+(sin(a-B)-0)^2
equation comes from the fact that the red line on the left is the same length as the red line on the right
in quad 2 the secant is negative and the tangent is positive
false
in quad 4 the cotangent is positive and the cosecant is negative
false
secant and tangent never have the same sign
false
sine and cosine never have the same sign
false
2*sqrt5/5
find the exact value of sin(tan-1(2))
cos=sec
pi, 2pi
sin(x)=1/2
pi/6, 5pi/6
1
simplify (cos^4(x)-sin^4(x))/(cos2x)
2sinxsiny
simplify cos(x-y)-cos(x+y)
0.23+/- 0.04
simplify tan(sin^-1(2/9))
0.31
simplify tan(sin^-1(3/10))
double angle formula
sin2x=2sinxcosx
sin(a+b)
sinAcosB+cosAsinB
sin(a-b)
sinAcosB-cosAsinB
false
t/f? sin^-1(sin(3pi/4))=3pi/4
even-odd identity
tan(-x)=-tan(x)
7sin(x)+x=1 solutions
there are two negative solutions and three positive solutions
cotangent and tangent always have the same sign where they are both defined
true
in quad 1 and 2 the tangent and cosine have the same sign where they are both defined
true
in quad 2 the sine is positive and the cosine is negative
true
in quad 4 the sine is negative and the secant is positive
true
the sine and the cosecant always have the same sign where they are both defined
true
1.23
use a calculator to find the value of the expression sec-1(3)
negative
when using the half angle formula to compute cos(17pi/12), will you use the positive root or negative root?
the inverse sine function is given by the equation y=sin^-1(x). find the equivalent
x=sin(y)
sin(pi/4)
√2/2
sin(pi/3)
√3/2