Download TRIGONOMETRIC FUNCTIONS (Review of Prerequisite Skills)

TRIGONOMETRIC FUNCTIONS
(Review of Prerequisite Skills)
CONCEPT REVIEW:
 SOH CAH TOA
 STANDARD POSITION
 RECIPROCAL TRIG RATIOS
1
csc  
sin 
1
sec  
cos 
1
cot  
tan 
 CAST RULE
(x,y)
r
θ
r=
x2  y2
S
A
T
C
(counterclockwise from +ve x-axis)
QUESTIONS:
1.
Evaluate each of the following to four decimal places:
a)
2.
sin 98 = __________
b)
cos 172 = __________
c)
tan 134 = __________
c)
sin A = 0.5726
Determine the measure(s) of  A in each of the following:
a)
cos A = – 0.2727
b)
tan A = 6.2136
3.
If sin θ < 0 and tan θ > 0, state the quadrant in which the terminal arm of θ is located.
4.
If sin  =
5.
Textbook exercises:
5
12
and cos  =
, determine the value of tan .
13
13
p.314 #1, 2 and p.386 #3ac
CONCEPT REVIEW:
 SPECIAL TRIANGLES
450
300
2
2
3
1
450
 PRIMARY TRIG GRAPHS
1
600
1
 TRANSFORMATIONS of TRIG GRAPHS
y  a sin(k (x  d))  c
amplitude
changes
period
changes
horizontal
translations
a 
(–) reflection
in the x-axis
3600
k
(–) reflection
in the y-axis
(+) left
(–) right
vertical
translations
(+) up
(–) down
QUESTIONS:
6.
Textbook exercises:
p.314 #3 – 6
7.
Determine the exact value of:
8.
Write an equation for each of the following:
a)
●
●
●
●
●
c)
● sine function
● maximum value of 5
● minimum value –1
sin 30o cos 30o + tan 60o sin 90o
sine function
amplitude 3 units
vertical displacement 2 units down
period 900
phase shift 450 to the right
CONCEPT REVIEW:
b)
●
●
●
●
●
cosine function
amplitude 5 units
period 7200
reflected in the horizontal axis
phase shift 300 to the left
QUOTIENT IDENTITIES:
 TRIGONOMETRIC IDENTITIES
sin 
cos 
cos 
cot  
sin 
tan  
PYTHAGOREAN IDENTITIES:
sin2θ + cos2θ = 1
1 + tan2θ = sec2θ
1 + cot2θ = csc2θ
QUESTIONS:
9.
Textbook exercises:
10.
Prove each of the following identities:
a)
p.386 #7
cos 
1  sin 
2


1  sin 
cos 
cos 
b)
sin2  tan2   tan2   sin2 
ANSWERS:
1.a) 0.9903
2.a) A = 1060, 2540
3. QIII
8.a) y = 3sin(4(x – 450)) – 2
b) –0.9903
b) A = 810, 2610
5
4. tan  =
12
b) y = –5cos(½(x + 300))
c) –1.0355
c) A = 350, 1450
5 3
7.
4
c) y = 3sinx