PreCal Test 3 Review
Sections 4.1 – 4.3, 5.1 – 5.4
March 10, 2011
Divide circle into 4 quadrants
Create three “tick marks” in each quadrant
Name the “Big 4”
Start with the middle tick mark and count by fourths while hitting Big 4
Count the remaining tick marks by counting by sixths while hitting Big 4
Fill in first quadrant with coordinates and remember All Students Take Calculus!
Right Triangle Trig (SOH CAH TOA)
Sin = opp/hyp
Csc = hyp/opp
Cos = adj/hyp
Sec = hyp/adj
Tan = opp/adj
Cot = adj/opp
Inverse Trig Functions
Sin-1(x)
D: [-1,1]
-1
Cos (x)
D: [-1,1]
-1
Tan (x)
D: all reals
Csc-1(x)
Sec-1(x)
Cot-1(x)
R: [-pi/2, pi/2]
R: [0, pi]
R: (-pi/2, pi/2)
D: (-inf, -1] U [1, inf)
D: (-inf, -1] U [1, inf)
D: all reals
R: [-pi/2, 0) U (0, pi/2]
R: [0, pi/2) U (pi/2, pi]
R: (0, pi)
PreCal Test 3 Review
Sections 4.1 – 4.3, 5.1 – 5.4
Suppose that θ is an acute angle of a right triangle and that
Suppose that θ is an acute angle of a right triangle and that
March 10, 2011
Find sec(θ) and csc(θ).
Find cos(θ) and csc(θ).
A car has wheels with a 22 cm radius. If each wheel’s rate of turn is 5 revolutions per second, how
fast is the car moving in units of cm/sec?
A car has wheels with a 14 inch radius. If each wheel’s rate of turn is 3 revolutions per second how
fast is the car moving in inches/sec?
PreCal Test 3 Review
Sections 4.1 – 4.3, 5.1 – 5.4
March 10, 2011
If the central angle θ defining the sector is given in degrees, then the area of the sector can be found
Use the formula above to find the area of the sector: θ = 160o, r = 6 cm.
using
Convert the following into radians:
7pi/4
14pi/15
Find three angles, two positive and one negative, that are coterminal with the given angle:
-2π
⁄3
Find three angles, two positive and one negative, that are coterminal with the given angle: 600.
Evaluate the following:
sin(
-2π
⁄3 )
cot(-45o)
sin (3000)
tan (3600)
tan (11pi/6)
sin (-7pi/6)
PreCal Test 3 Review
Sections 4.1 – 4.3, 5.1 – 5.4
March 10, 2011
Find the exact value of the following expression. If undefined, state undefined.
Sin-1 (-1/2)
Tan-1 (sqrt(3))
Cos-1 (0)
Find the exact value of the following expression. If undefined, state undefined.
Find the phase shift for the following function:
On which interval is f(x) = 8 sin (x) increasing?
On which interval is f(x) = 5 cos (x) decreasing?
Find the period for the following function:
PreCal Test 3 Review
Extra Problems:
Sections 4.1 – 4.3, 5.1 – 5.4
March 10, 2011