Trigonometry Flashcards
Sin(pi-x) =
-Sin(x)
Cos(2pi - x) =
Cos(x)
Sin(90-x) =
Cos(x)
Period of sin = Period of cos =
2*pi
Period of tan =
pi
tan(1.25pi) = tan(0.25pi)
Not all values of theta if and only if
dividing by zero
radians > degrees
ranges of trig
3sin^2(x) + 2sinxcosx + cos^2x =
3tan^2x + 2tanx + 1
How many solutions to (3+cosx)^2 = 4-2sin^8x
LHS range is 4-16
RHS range is 2-4
Therefore one solution when x=4
Consider the range of the trig functions
-1 - 1
0 - 1
Divided by sin/cos/sin^2x/cos^2x
to find a quadratic
Sin^n(a) range changes only when
n=2x not when a changes
Cos(2pi - x) =
cosx = sin(90 - x)
(3+cosx)^2 = 4-sin^8(x)
LHS varies from 4-16
RHS varies from 2-4
therefore only one solution of 4
sin(pi - x) =
sin(-x) = -sin(x)
max/min of trig:
0 < (3sin^2(7x+11)) < 3
Trig has multiple solutions –>
check domain
Simultaneous equations with trig –>
think of identities
Trig equalities: simplify, think of ranges + identities
2^(-x^2), 2^(2x-x^2) stationary point
tanX = q/p
p^2 - 4pq + q^2 = 0
(p/q)^2 - 4(p/q) + 1 = 0
Two solutions for trig, sin2x…
When relating angles/lengths use shared lengths/angles
trig –> ranges
CosX, sinX –> cosXCosX + sinXSInX = 1
sin^2(x) + 3sinxcosx + 2cos^2x = 0
cosx =/= 0 therefore divide by cos^2(x)
tan^2(x) + 3tanx(x) + 2 = 0
sin(x) < x
check domains for amounts of solutions
