Vocab and Basics
Other Trig Functions
Unit Circle and Radians
Arc Length and Area
Solving and Logic
100
What quadrant is 928o in?
928 - 360 = 568
568 - 360 = 208
Quadrant 3 (between 180 and 270)
100
The point (-4/5, -3/5) lies on the unit circle. Find the value of secx
secx = 1/cosx = 1/(x value on unit circle) = -5/4 or -1.25
100
convert 135o to radians. Give your answer in terms of pi
(3pi)/4
100
Find the arc length: Circle with radius of 20 feet. Central angle of 75o. Round to two decimal places if needed.
1. convert 75o to radians
2. s =
r*theta = (5pi)/12 * 20
Answer: 26.18 feet
100
Where is tanx undefined? (Different wording, same question: What x values do not have tangent values?)
90 and 270
or
pi/2 and (3pi)/2
200
Angle of
(16pi)/3
Find a coterminal angle between 0 and
2pi
(4pi)/3
200
In which quadrants is cosecant (csc) positive?
Quadrant 1 and Quadrant 2 (same place sin is positive)
200
Convert to degrees. Round to the hundredths.
(17pi)/19
161.05o
200
Find the area of the sector: Circle with radius of 20 feet. Central angle of 75o. Round to two decimal places if needed.
A=1/2*theta*r^2
75*pi/180=(5pi)/12
A=1/2*(5pi)/12*20^2
(250pi)/3=261.79938 ft^2
200
If cos u = 1/3 and tan u < 0, find the value of u in degrees. Round to two decimal places
cos-1(1/3) = 70.53o but tan < 0 so should be in quadrant 4.
reference angle 70.53o
actual angle u = 360 - 70.53 = 289.47o
300
Find the reference angle for
(16pi)/3
pi/3
300
Which quadrant has cosx < 0 and cotx > 0?
Quadrant 3
300
Find the reference angle for
(49pi)/11
This angle is in quadrant 1 with reference angle of (5pi)/11
2pi = (22pi)/11
(49pi)/11-(22pi)/11=(27pi/11)
(27pi)/11-(22pi)/11=(5pi/11)
(5pi)/11<pi/2
300
A is the center of a circle. The length of the segment BD is 42 inches and the length of arc CD is 7pi inches. Find the measure of the central angle of the shaded sector.
60o or pi/3
300
Find sinx and tanx if cosx = -3/5;
pi < x< (3pi)/2
sinx = -4/5 and tanx = 4/3
400
Find a positive coterminal angle for -999o
81o
400
If (-2, 5) is a point on the terminal side of angle u, find the exact value of csc(u).
radius =
sqrt(29)
csc(u) =
1/sin(u)
=
sqrt(29)/5
400
Give a negative coterminal angle for
(453pi)/6
-pi/2
400
The area of the circle shown is 60pi in2. the area of the shaded sector is 48pi in2. Find the measure of the missing angle, in degrees.
72o
400
Use identities to solve: If tanx = 0.97 and sinx = -0.9, then cosx = ?
Round to nearest hundredth.
0.93
500
An angle in standard position goes through the point (-5, 7). Find the cosine value of the angle
radius/hypotenuse is NOT 1 so we need pythagorean theorem.
sqrt((-5)^2+7^2)=sqrt(25+49)=sqrt74
cosine = adjacent/hypotenuse
adjacent = -5
cos(theta)=-5/sqrt(74)
500
If cotx = -3 and sinx > 0, then secx = ?. Round to two decimal places
cotx < 0 and sinx>0 means x is in quadrant 2 and secx < 0
cotx = -3 --> tanx = -1/3 --> tan-1(-1/3) =-18.43o
Reference angle = 18.43.
sec(18.43) 1/cos(18.43) = 1.05 but said in quadrant 2, secx is negative
final answer: - 1.05
500
Calculate
sin((57pi)/4)
Reference angle:
(57pi)/4-(8pi)/4*7=pi/4
(57pi)/4 is in Quadrant 1 (is own reference angle)
so sin((57pi)/4)=sin(pi/4)=sqrt(2)/2
500
The circumference of the circle shown is 100 units and the measure of the central angle of she shaded sector is given by theta = pi/12 .Find the arc length of the shaded section.
pi/12 is 1/24 of the whole circle. So the arc length would be 1/24 of the circumference or 1/24 * 100 = 100/24 = 4.1666... units
500
Solve for x: sin2x - 3sinx + 2 = 0
90 degrees or pi/2 radians