Identities and Properties for Unit 3 Precalc

csc0

1/sin0 —> reciprocated

sec0

1/cos0

cot0

1/tan0

tan0

sin0/cos0

cot0 (sin and cos terms)

csc0/sec0 —→ cos0/sin0

sin²0 + cos²0 = ?

sin²0 + cos²0 = 1

tan²0 + 1 = ?

tan²0 + 1 = sec²0

1 + cot²0 = ?

1 + cot²0 = csc²0

cos-1(x) =

cos^-1(x) = sin-1 sqrt(1 - x²)

sin-1(x) =

cos-1(sqrt(1-x²))

sin(-0) =

-sin0

cos(-0)

cos0

tan(-0)=

-tan0

csc(-0)=

-csc0

sec(-0)=

sec0

cot(-0)

-cot0

sin(pi+0) =

-sin0

cos(pi+0)

-cos0

tan(pi + 0)

-sin0/-cos0 = —> tan0

sin(pi-0)

sin0

cos(pi-0)

-cos0

tan(pi-0)

sin0/-cos0 = —> -tan0

sin0 = ____(90 - 0)

sin0 = cos(90 - 0)

cos0 = ___ (90-0)

cos0 = sin(90-0)

tan0 = ____(90 - 0)

tan = cot(90-0)

cot0 = ____ (90 - 0)

cot = tan(90-0)

sin(a + B) =

= cosa(sinB) + sina(cosB)

cos(a + B) =

cosa(cosB) - sina(sinB)

tan(a + B) =

(tana + tanB)/ 1-(tana)(tanB)

sin(a-B) =

sina(cosB) - sinB(cosa)

cos(a-B)

cosa(cosB) + sina(sinB)

tan(a-B)

(tana - tanB)/ 1+ tana(tanB)

sin(20) =

2 sin0cos0

cos20 =

cos²0 - sin²0

cos20 =

1 - 2sin²0

cos20 =

1-2sin²0

tan20

(2tan0)/1-tan²