Unit 1 Exam
Define the points that divide the unit circle into 8 equal arcs
0 pi/4 pi/2 3pi/4 pi 5pi/4 3pi/2 7pi/4 2pi
What values of (x,y) correspond with 11pi/6 on the unit circle?
(root3/2, -1/2)
The Pythagorean identity of tan and sec
1 + tan^2 = sec^2
Unit Circle Equation
x^2 + y^2 = 1
What values of (x,y) correspond with pi on the unit circle?
(-1,0)
What values of (x,y) correspond with 4pi/3 on the unit circle?
(-1/2, -root3/2)
What values of (x,y) correspond with 2pi/3 on the unit circle?
(-1/2, root3/2)
What values of (x,y) correspond with 7pi/6 on the unit circle?
(-root3/2, -1/2)
What values of (x,y) correspond with 5pi/6 on the unit circle?
(-root3/2, 1/2)
What values of (x,y) correspond with 3pi/2 on the unit circle?
(0,-1)
What values of (x,y) correspond with pi/2 on the unit circle?
(0,1)
What values of (x,y) correspond with 0 on the unit circle?
(1,0)
What values of (x,y) correspond with 2pi on the unit circle?
(1,0)
What values of (x,y) correspond with 5pi/3 on the unit circle?
(1/2, -root3/2)
What values of (x,y) correspond with pi/6 on the unit circle?
(root3/2, 1/2)
Define the points that divide the unit circle into equal 12 equal arcs
0 pi/6 pi/3 pi/2 2pi/3 5pi/6 pi 7pi/6 4pi/3 3pi/2 5pi/3 11pi/6 2pi
tan 45 degrees = tan pi/4 = ___
1
cos 60 degrees = cos pi/3= ___
1/2
sin 30 degrees = sin pi/6 = ___
1/2
The reciprocal identity of sec theta =
1/cos
The reciprocal identity of tan theta =
1/cot
The reciprocal identity of sin theta =
1/csc
The reciprocal identity of cos theta =
1/sec
The reciprocal identity of csc theta =
1/sin
The reciprocal identity of cot theta =
1/tan
definition of sec t given point (x,y) on the unit circle
1/x, undefined if x = 0
definition of csc t given point (x,y) on the unit circle
1/y, undefined if y = 0
If theta is an angle in standard position and (x,y) is a point on its terminal side, r = __________
square root of (x^2+y^2)
What values of (x,y) correspond with pi/3 on the unit circle?
(1/2, root3/2)
Which trig functions are even?
Cosine and secant cos (-t) = cos t sec (-t) = sec t
Cofunctions of complementary angles are _____.
Equal
Which trig functions are odd?
Sin, tan, csc, cot sin(-t) = -sin t
In a right triangle, theta lies in the first quadrant and therefore the value of each trig function is ________.
Positive
Given the acute angle theta, the acute angle theta' formed by the terminal side of theta and the horizontal axis
Reference angle
If theta is an angle in standard position and (x,y) is a point on its terminal side, r = square root of (x^2+y^2), sec =
r/x (x cannot = 0)
If theta is an angle in standard position and (x,y) is a point on its terminal side, r = square root of (x^2+y^2), csc =
r/y (y cannot = 0)
cos 45 degrees = cos pi/4 = ___
root2/2
sin 45 degrees = sin pi/4 = ___
root2/2
tan 60 degrees = tan pi/3 = ___
root3
cos 30 degrees = cos pi/6 = ___
root3/2
sin 60 degrees = sin pi/3 = ___
root3/2
tan 30 degrees = tan pi/6 = ___
root3/3
Arc Length Formula
s = r * theta
What are the sign rules for an angle with its terminal side in Quadrant I?
sin = + cos = + tan = +
What are the sign rules for an angle with its terminal side in Quadrant II?
sin = + cos = - tan = -
What are the sign rules for an angle with its terminal side in Quadrant IV?
sin = - cos = + tan = -
What are the sign rules for an angle with its terminal side in Quadrant III?
sin = - cos = - tan = +
The quotient identity of tan theta =
sin/cos
The Pythagorean identity of sin and cos
sin^2 + cos^2 = 1
if theta is pi/6 radians it is ___ degrees
30
if theta is pi/4 radians it is ___ degrees
45
if theta is pi/3 radians it is ___ degrees
60
In a right triangle, the angle theta lies between the numerical values 0 degrees and __ degrees.
90
In a right triangle, cos theta is equal to
adj/hyp
In a right triangle, cot theta is equal to
adj/opp
The quotient identity of cot theta =
cos/sin
In a right triangle, sec theta is equal to
hyp/adj
In a right triangle, csc theta is equal to
hyp/opp
In a right triangle, tan theta is equal to
opp/adj
In a right triangle, sin theta is equal to
opp/hyp
definition of cos t given point (x,y) on the unit circle
x
If theta is an angle in standard position and (x,y) is a point on its terminal side, r = square root of (x^2+y^2), cos =
x/r
If theta is an angle in standard position and (x,y) is a point on its terminal side, r = square root of (x^2+y^2), cot =
x/y (y cannot = 0)
definition of cot t given point (x,y) on the unit circle
x/y, undefined if y = 0
definition of sin t given point (x,y) on the unit circle
y
If theta is an angle in standard position and (x,y) is a point on its terminal side, r = square root of (x^2+y^2), sin =
y/r
If theta is an angle in standard position and (x,y) is a point on its terminal side, r = square root of (x^2+y^2), tan =
y/x (x cannot = 0)
definition of tan t given point (x,y) on the unit circle
y/x, undefined if x = 0
