Unit 6 Pre calc
Domain of sine and cosine
(-infinity, infinity)
Find the Exact value of the expression without a calculator tan 5pi/3
(5pi/3)*(180/pi)=300 360-300=60 All Students Take Calc =-tan60 =-square root of 3
Quotient Identity of cot t =
(cos t)/(sin t)
Equation to convert degrees to radians
(pi radians)/180
Quotient Identity of tan t =
(sin t)/(cos t)
pythagorean identity (cot and csc)
1 + cot^2t = csc^2t
coterminal angles in radians ex. 22pi/3
1) common denominator 2pi/1=6pi/3 2) subtract (possibly more than once) (22pi/3)-(6pi/3)=(16pi/3)-(6pi/3)=(10pi/3)-(6pi/3)=4pi/3
Finding the length of a circular arc ex. radius=10, central angle is 120
1) convert degrees to radians ex. 120*(pi radians/180)=2pi/3 2) s=r(theta) ex. s=10(2pi/3) =20pi/3
Find the Exact value of the expression without a calculator sin(2pi/3)
1) find reference angle (2pi/3)*(180/pi)=120 180-120=60 2) all students take calc. Is it positive? =sin60 3) sine of 30 60 90 triangle = square root of 3/2
sin t= 3/5 and 0<t<pi/2
1) find the quadrant 2) find the right pythagorean identity sin^2t + cos^2t = 1 3) plug in numbers and solve sin^2t + cos^2t = 1 (3/5)^2+cos^2t=1 9/25+cos^2t=25/25 (25/25)-(9/25)=16/25 cos^2t=16/25 square root cos^2t=+ or - 4/5 + because of the quadrant =4/5
pythagorean identity (tan and sec)
1+tan^2t=sec^2t
Reciprocal of sec t
1/cos t
Reciprocal of tan t
1/cot t
Reciprocal of sin t
1/csc t
Reciprocal of cos t
1/sec t
Reciprocal of csc t
1/sin t
Reciprocal of cot t
1/tan t
Equation to convert radians to degrees
180/(pi radians)
Finding a cofunction with the same value as the given expression sin72
It is the cofunction (90-theta) or (pi/2- theta) ex. sin72=cos(90-72) = cos18
Reciprocal of sine
cosecant (csc)
Cofunction of sine
cosine
Quadrant 4
cosine and secant positive
Cofunction of tangent
cotangent
reciprocal of tangent
cotangent (cot)
Reciprocal of cosine
secant (sec)
What trig functions are odd?
sin(-t)=-sin t and tan(-t)=-tan t and csc(-t)=-csc t and cot(-t)=-cot t
pythagorean identity (sin and cos)
sin^2t + cos^2t = 1
Quadrant 2
sine and cosecant positive
Initial side of an angle
starting position of the rotated ray in the formation of an angle
Quadrant 3
tangent and cotangent positive
Range of sine and cosine
[-1,1]
Quadrant 1
all positive
What trig functions are even?
cos(-t)=cos t and sec(-t)=sec t
cofunction of secant
cosecant
In a unit circle the radian measure or the central angle is equal to
the length of the intercepted arc
Terminal side of an angle
the ray where measurement of an angle stops
reference angle ex. theta=345
the smallest angle between the terminal side and the x-axis 360-345=15
coterminal angles ex. 420
theta+or-360= coterminal angles 420-360=60
Equation to find the radian measure
theta=s/r