Fall 2010 Math 151
Week In Review: Thursday Sept. 2, 2010
Instructor: Jenn Whitfield
1. Fill in the side lengths for the standard 30-60-90 and
45-45-90 triangles, then complete the given chart.
30° 45° θ
30° =
45° =
60° =
Sin θ
π
6
π
4
π
3
Cos θ
Tan θ
7. Draw θ = 228° in standard position. Find the
reference angle, α. Label θ and α.
8. Given θ = 210D ,
a) convert θ to radians.
b) Find the exact values of the six trigonometric
functions of θ .
9. Find all values of θ, that satisfy the equations below.
a) 9cos θ – 2 = 0 , for 0 ≤ θ ≤ 2π
b) 2cos θ + sin 2θ = 0
10. Graph each of the six trig functions on [−2π , 2π ] .
Verbally describe the behavior of each graph.
11. Prove the identities below.
⎛π
⎞
a) sin ⎜ + x ⎟ = cos x
2
⎝
⎠
b) (sin x + cos x) 2 = 1 + sin(2 x)
c) 2csc(2t ) = sec t csc t
2. Fill in all blanks on the unit circle below.
Important Trig Facts
• π radians = 180°
a
• θ = , where θ is the central angle with radius r
r
and subtended arc a.
Trig Ratios
opp
adj
sin θ =
cos θ =
hyp
hyp
hyp
hyp
cscθ =
secθ =
opp
adj
opp
adj
adj
sin θ =
opp
tan θ =
Trig Identities
1
1
1
cscθ =
secθ =
cot θ =
sin θ
cosθ
tan θ
sin θ
cosθ
tan θ =
cot θ =
cos θ
sin θ
2
2
sin θ + cos θ = 1
sin( x + y ) = sin x cos y + cos x sin y
3. Find the quadrant in which each angle lies.
7π
11π
31π
a)
b) −
c)
6
3
4
4. Find the reference angle for each of the following.
7π
2π
b) −
6
3
5. Convert 81° to radians.
a)
c) 231D
6. Find two angles that are coterminal to -
5π
.
8
sin( x − y ) = sin x cos y − cos x sin y
cos( x + y ) = cos x cos y − sin x sin y
cos( x − y ) = cos x cos y + sin x sin y
tan x + tan y
1 − tan x tan y
tan x − tan y
tan( x − y ) =
1 + tan x tan y
sin(2 x) = 2sin x cos x
tan( x + y ) =
cos(2 x) = cos 2 x − sin 2 x = 2cos 2 x − 1 = 1 − 2sin 2 x