Trig Exam 3

Three Pythagorean Identites

Sin²θ+Cos²θ=1, Cot²θ+1=Csc²θ, 1+ tan²θ= Sec²θ

Sin 2v

2sinvcosv (2 in front sin and cos v)

Cos 2v (1)

Cos²v-sin²v

Cos 2v (2)

2cos²v-1

Cos 2v (3)

1-2sin²v

cos (u-v)

cos u cos v + sin u sin v

Sin (u+v)

sin u cos v + cos u sin v

sin (u-v)

sin u cos v - cos u sin v

cos (u + v)

cos u cos v - sin u sin v

Cos u/2

± square root, 1+ cosv (over) / 2

Sin u/2

± square root, 1- cosv (over) / 2

tan x= 1/ square root of 3

pi / 6, 5pi/6

Quadratic Type Equations: 2 sin²x-sinx -1=0

Use the quadratic formula, (sin²x=x²), sinx = 1 or sinx = -1/2 find the angles that match that

Solving Trig Equations: If it has different trig functions?

change the functions to match.

Help with solving for angles U and V

Sin²0+cos²0=1, you can use the formula x²+y²=r², solve for the missing numbers then plug in

x²+y²=r²

remember x= cos y= sin, r= hyp

SOH CAH TOA

Sin= opp/hyp, Cos, Adj/hyp, Tan opp/ adj

Sec / Sec²x

reciplacal of cos = hyp/adj, 1/sec²x = cos²x

Csc / Csc²x

reciplacal of sin = hyp/opp, 1/csc²x= sin²x

Cot / Cot²x

the recipcal of tan = adj/opp, 1/cot²x = tan²x

Quadratic formula

(-) b +- square root (b)²-4(a)( c ) / 2 (a)

Remember when dividing two fractions so ½ over 1/3

you multiply, cancel out the ones that match and you are left with you answer.

tan x/2 = square root 3 over 3 or 1/ square root 3

pi over 6, 7 pi over 6