precal
cos(2x)/1+sin(2x)=(cotx-1)/cotx+1
((cosx-sinx)/sinx)/((cosx+sinx)/sinx)
tan(2x)
(2tanx)/1-tan^2x
(2cos^2x-1)^2/cos^4x-sin^4x=1-2sin^2x
(cos^2x-sin^2x)^2/cos^2x-sin^2x
exact value: sin(17pi/12)
(root6-root2)/4
exact value: arcsin(sin(-3pi/7))
-3pi/7
exact value: ((sin-20)/cos380)+tan200
0
Exact Value of csc450
1
exact value of cot(17pi/4)
1
exact value: sin(arcsin(-4/5)-arctan(3/4))
1
sin(pi-x)=sinx
1(sinx)
1+cot^2(-x)=csc^2x
1+cot^2x
1+tanx/1-tanx=cotx+1/cotx-1
1+tanx/1-tanx(cotx/cotx)
csc(2x)=(1/2)secxcscx
1/2sinxcosx
quadrant of: secx<0, sinx>0
2
solve on (0,2pi): cos(x/3-pi/4)=1/2
21pi/12
cosx=((1-tan^2(x/2))/(1+tan^2(x/2)))
2cosx/2
exact value: arcsec(-2)
2pi/3
exact value: sec(-pi/6)
2root3/3
sin(2x)
2sinxcosx
write trig exp: cos(arcsosU+arcsinV)
U(root(1-v^2))-U(root(1-u^2))
a)sin(a+b) b)cos(a+b), c)sin(a-b), d)tan(a-b) sina=5/13; -3pi/2<a<-pi, tanb=-root3; pi/2<b<pi
a)(5+12root3)/26 b)(12-5root3)/26 c)(5-12root3)/26 d)(-240-169root3)/69)
cos(2x)
cos^2x-sin^2x
secx-tanx=(cosx/1+sinx)
cos^2x/cosx+sinxcosx
write as trig exp: cos(arccsc(u))
cosx(root(u^2)-1/u)
cscx-1/cotx=cotx/cscx+1
cot^2x/cotx(cscx+1)
exact value: tan(arctan(pi))
pi
exact value: arcsin(root2/2)
pi/4
cos(x/2)
root(1+cosx/2)
tan(x/2)
root(1-cosx/1+cosx)
sin(x/2)
root(1-cosx/2)
exact value: cos(-30)
root3/2
exact value: (tan40-tan10)/1+tan40tan10
root3/3
exact value: sec(arcsin(2root5/5))
root5
Remaining 6: cosx=(-4/5), x in Q3
sinx=(-3/5) tanx=(3/4) cotx=(4/3) secx=(-5/4) csc=(-5/3)
sinxcosx/cos^2x-sin^2x=tanx/1-tan^2x
sinxcos^2x/cosx(cos^2x-sin^2x)
solve on (0,2pi): (root3x)+1=0
x=(2pi/3), (11pi/6)
solve on (0,2pi): cos^2x-sin^2x=1+cosx
x=(pi/2, 7pi/6, 11pi/6)
solve on (0,2pi): sin(3x)=-1
x=(pi/2, 7pi/6, 11pi/6)
solve on (0,2pi): cosx=-sin(-x)
x=(pi/4, 5pi/4)
exact value: arcos(sin(5p/4))
x=3pi/4
exact value: sec(arctan(1/2))
x=root5/2
find inverse: f(x)=2cos(3x+2); -2/3<x<-2/3+pi/3
y=((arcos(x/2)-2)/3)
find inverse: f(x)=2tanx-3; -pi/2<x<pi/2
y=arctan((x+3)/2)
