PRACTICE
Evaluate each expression.
(1) tan(30°) + cot
(3) sec
_______
+ csc(210°) _______
PRACTICE
(4) 3 csc
_______
_______
Evaluate each expression.
(5) sec (45°) − tan (45°)
(7) csc
− cot
PRACTICE
(2) sec(360°) − cot
_______
_______
(6) sec
(8) csc
− tan
_______
− cot (60°)
_______
Consider your answers in #5—8.
(9) Does the identity sec 𝜃 − tan 𝜃 = 1 appear to be true in #5—6?
(10) Pick an additional value for theta (θ).
Verify that the identity is true for that value.
VERIFICATION:
(11) Does the identity csc 𝜃 − cot 𝜃 = 1 appear to be true in #7—8?
(12) Pick an additional value for theta (θ).
Verify that the identity is true for that value.
VARIATIONS
ON THE
PYTHAGOREAN
IDENTITY
_________
_________
VERIFICATION:
A sec 𝜃 =
C csc 𝜃 =
B tan 𝜃 =
D cot 𝜃 =
PRACTICE
(13) Show how the original Pythagorean identity (sin 𝜃 + cos 𝜃 = 1) can be manipulated in
order to form identity A or B in the table above.
MANIPULATION:
PRACTICE
(14) Show how the original Pythagorean identity (sin 𝜃 + cos 𝜃 = 1) can be manipulated in
order to form identity C or D in the table above.
MANIPULATION:
PRACTICE
Use the six trigonometric ratios (sin, cos, tan, sec, csc, cot) and/or the variations of the
Pythagorean identity to construct each proof.
(15)
= cos 𝜃
PROOF:
(16)
= csc 𝜃 + cot 𝜃
PROOF:
(17) sin 𝜃 = (1 − cos 𝜃)(1 + cos 𝜃)
PROOF:
(18) tan 𝜃 csc 𝜃 = sec 𝜃
PROOF:
(19) csc 𝜃 tan 𝜃 − 1 = tan 𝜃
PROOF:
(20) (1 − cos 𝜃)(csc 𝜃) = sin 𝜃
PROOF:
(21) (sin 𝜃 + cos 𝜃) + (sin 𝜃 − cos 𝜃) = 2
PROOF:
(22) If the graph of 𝑦 = (𝑥 + 4) − 3 is shifted down 5 units
and to the left 2 units, write an equation that represents the new parabola. _________________
REVIEW
REVIEW
There are currently 1700 cooties in Mr. Fitzgibbon’s classroom. Every day, the number of
cooties increases by 130.
(23) Write an equation that models this scenario.
(24) How many cooties
will there be in nine days? ________
______________________
(25) How many days will it take for
the number of cooties to reach 5600? ________
REVIEW
REVIEW
Consider the
function 𝑓(𝑥) = 2𝑥 − 200.
(28) Which set of points represents the
x-intercepts of the function 𝑦 = 2𝑥 + 9𝑥 − 5?
(26) Find
its roots. ______ ______
a) (1/2,0) (—5,0)
b) (—1,0) (5,0)
c) (1,0) (—5,0)
(27) Sketch its graph. Label
at least one additional point.
d) (—1/2,0) (5,0)
REVIEW
(29) Write an exponential equation for the
curve that passes through the points (1,12) and (3,108). ________________
REVIEW
(30) Write an arithmetic equation for the
line that passes through the points (1,12) and (3,108). ________________
REVIEW
Evaluate each expression without a calculator.
(31) log
/
_______
(32) log 128
_______
REVIEW
(35) Which of the following
expressions is NOT equivalent to √𝑥 ?
REVIEW
(34) 2 ∙ log 7
_______
a) (𝑥 )
c) 𝑥
/
/
_______
b) 𝑥
/
d) 𝑥
If log 3 ≈ 0.68 and log 2 ≈ 0.43, approximate the decimal value of each expression:
(36) log 12 _______
(37) log 32 _______
(39) If x is a real number, for what
values of x is the equation
true?
REVIEW
(33) log 1
(38) log
_______
a) all values of x
b) only x=3
c) only x=0
d) no values of x