PRACTICE
Consider the right triangle pictured at right.
(1) Find sin 𝜃. ________
(2) Find cos 𝜃. ________
c
(3) Find tan 𝜃. ________
a
Θ
b
(4) Find
. ________
(5) What do you observe
about your answer to #4? ______________________________________
PRACTICE
Using the tangent ratio established in the previous problem and the values from the unit
circle, determine the exact value of each expression.
(7) tan(150) _______
(8) tan(180) _______
(9) tan(300) _______
(10) tan
(11) tan(240) _______
(12) tan
(13) tan(360) _______
(6) tan
PRACTICE
_______
_______
_______
(14) tan
_______
(15) On the unit circle, in which quadrants is tangent positive? ________________
How do you know? _______________________________________________________________
SEC
CSC
COT
(“SECANT”)
(“COSECANT”)
(“COTANGENT”)
PRACTICE
(16) sec
Use the functions defined above to find the exact value of each expression.
________
(17) sec(135) ________
(18) sec(2𝜋) ________
(19) sec(210) ________
(20) sec
(21) sec(300) ________
(22) csc
(23) csc(315) ________
(24) csc(𝜋) ________
(26) csc(60) ________
(27) csc
(28) cot(240) ________
(29) cot
(30) cot(45) ________
(31) cot
(32) cot(180) ________
(25) csc
________
________
________
________
________
(33) cot
________
________
PRACTICE
Determine which values of theta (in degrees) yield undefined values of each function below.
Then prove your responses in the space provided.
(34) sec 𝜃 is undefined when 𝜃=___________
(35) csc 𝜃 is undefined when 𝜃=___________
DEGREES
DEGREES
PROOF:
PROOF:
(36) tan 𝜃 is undefined when 𝜃=___________
(37) cot 𝜃 is undefined when 𝜃=___________
DEGREES
DEGREES
PROOF:
PROOF:
PRACTICE
(38) Which of the following expressions is not undefined?
a) sec(𝜋)
b) csc(2𝜋)
c) tan
d) cot(𝜋)
PROOF:
PRACTICE
(39) Which of these expressions is equivalent to tan
a) 0
b) 1
?
c) ∅
d) —1
c) √3
d) −√3
PROOF:
PRACTICE
(40) What is cos
a) 0
+ sin(240)?
b) 1
PROOF:
PRACTICE
(41) Use substitution to prove that tan(𝜃) cot(𝜃) sec(𝜃) cos(𝜃) = 1.
PROOF:
PRACTICE
(42) Use substitution to prove that tan(𝜃) sec(𝜃) sin(𝜃) = tan 𝜃.
PROOF:
REVIEW
Determine whether each statement is true or false. Circle T for true or F for false.
(43) sin
π
3
> cos(150°)
T
(44) cos(2π) ≥ sin(0°)
F
PROOF:
REVIEW
Consider the steps in the incorrect
solution process shown at right.
(46) What is the correct solution? _______
(47)
(49)
REVIEW
REVIEW
F
PROOF:
(45) In which step is the first error made? _______
REVIEW
T
STEP 1:
log (𝑥 ) − log (𝑥) = 1
STEP 2:
log
STEP 3:
𝑥 =1
STEP 4:
√𝑥 = √1 STEP 5:
𝑥=1
=1
Simplify each expression.
÷
_________
_________
(51) Solve the system:
𝑥 − 2𝑦 + 3𝑧 = 14
𝑥 + 3𝑦 + 2𝑧 = −1
2𝑥 − 4𝑦 − 3𝑧 = 1
(48)
∙
(50)
+
_________
_________
_____________
Solve each equation.
(52) 3√3𝑥 + 4 − 2 = 13
(53) −3(𝑥 + 2) + 7 = −20 ______ ______
_______
(54) 𝑥 − 3𝑥 = 10 ______ ______
(55) 3𝑥 − 6𝑥 − 1 = 0 _____________
(56) −3|𝑥 − 3| + 1 = −20 ______ ______
(57) 6(𝑥 − 1) + 2 = 50 _______
REVIEW
(58) Which value is
not equivalent to sin(
2π
)
3
?
11π
)
6
a) cos(
7π
6
b) cos( )
π
3
c) sin( )
π
6
d) cos( )