Test 3 Flashcards
how to get 1 from sin & cos
1 = sin² + cos²
how to get 1 from sec & tan
1 = sec² - tan²
how to get tan from sin & cos
tan = sin/cos
how to get cot from sin & cos
cot = cos/sin
cos(α + β)
cosαcosβ - sinαsinβ
cos(α - β)
cosαcosβ + sinαsinβ
sin(α + β)
sinαcosβ + cosαsinβ
sin(α - β)
sinαcosβ - cosαsinβ
tan(α + β)
(tanα + tanβ)/(1 - tanαtanβ)
tan(α - β)
(tanα - tanβ)/(1 + tanαtanβ)
sin2θ
2sincos
cos2θ with sin & cos
cos² - sin²
sin(α/2)
± √((1 - cosα)/2)
cos(α/2)
± √((1 + cosα)/2)
tan(α/2)
± sinα/(1 + cosα)
cos2θ with sin
1 - 2sin²
cos2θ with cos
2cos² - 1
how to go about solving for (trig fⁿ)² = ratio
a) answer it as ±(trig fⁿ)⁻¹(ratio)
b) then you will have 4 answers all around the Q’s
how to go about solving for (trig fⁿ)(nθ) = ratio
a) Find the 2 angles θ would be without division.
b) Write out 2 formulas that look like this: 2θ = (angle 1 or 2) + 2πk
c) Divide and get θ = (angle 1 or 2)/2 + πk
d) Keep adding πk to each of the 2 angles until you reach below the limit θ has to be in
how to go about solving for (trig fⁿ) = decimal in a certain quadrant
a) Find the sign of the trig fⁿ when it’s in the quadrant you have to solve for
b) Plug (trig fⁿ)⁻¹(decimal) into calc to find your first answer, θ
c) Subtract θ from π if the same-sign value is on top; subtract it from 2π if the same-sign value is on bottom.
how to go about solving for (trig fⁿ) = (different trig fⁿ)
a) Try to turn them into multiples by manipulating the equation
b) Set those multiples equal to 0
c) Solve for each angle in the trig fⁿs
what to do if you find yourself stuck on an identity
look for conjugates. anywhere.
how to get 1 from cot & csc
1 = csc² - cot²
