Trigonometric equations Flashcards
What is 1 / sinx ?
cosec x
(cosectant)
What is 1 / cos x?
sec x
(sectant)
What is 1 / tanx?
cot x
cotangent
cos x / sin x
Learn the graphs for:
y = cosec x
y = sec x
y = cot x
Do it
Learn the trig identity relating sin2x and cos2x
sin2x + cos2x = 1
Learn the trig identity relating tan2x and sec2x
tan2x + 1 = sec2x
Learn the trig identity including cot2x and cosec2x?
1 + cot2x = cosec2x
Why can the inverse of y = sin/cos/tan x not be found without restrictions of the domain?
All of them are not one-to-one mapping
Therefore must just take a section of the domain
What are the restrictions that are taken of sin/cos/tan x for the graph of their inverse?
sinx: -90 <= x <= 90
cosx: 0 <= x <= 180
tanx: -90 <= x <= 90
How do you find the inverse of a graph?
Refelct a graph in the line y=x
Write the formula for sin(A+B)
sin(A+B) = sinAcosB + cosAsinB
Write the formula for sin(A-B)
sinAcosB - cosAsinB
Write the formula for cos(A+B)
cosAcosB - sinAsinB
Write the formula for cos(A-B)
cosAcosB + sinAsinB
Write the formula for tan(A+B)
tan(A+B) = (tanA + tan B) / (1 - tanAtanB)
Write the formula for tan(A-B)
tan(A-B) = (tanA - tanB) / (1 + tanAtanB)
Learn the double angle formula for sin2A
sin2A = 2sinAcosA
Learn the double angle formulae for cos2A
cos2A = cos2A - sin2A
cos2A = 2cos2A - 1
cos2A = 1 - 2sin2A
Learn the double angle formula for tan2A
tan2A = 2tanA / (1-tan2A)
What do you do if the question asks you to write an equation in the form Rcos(2x+a)?
Expand to get R(cos2xcosa - sin2xsina)
(Rcosa)cos2x - (Rsina) sin2x
Then relate back to left hand side as things in the bracket must equal the constants on that left hand side
Calculate a using these values
Square (Rcosa) = constant from LHS and (Rsina) = constant from LHS
Add them together and use (sin2x + cos2x) to get R2 = Sum of LHS constants2
How do you convert sin2x/2 be converted to a form with just x?
Double angle formula, in this case x is double
cos x = 1 -2sin2x/2
