See the attached file for questioins
Thehonest
2.docExam 769700
1.
Find the complete exact solution of
sinx = − 3 2
sinx=-
3
2
2.
Solve
cos2x − 3sinxcos2x = 0
cos2x-3sinxcos2x=0
for the principal value(s) to two decimal places.3.
Solve
tan2 x + tanx −1= 0
tan
2
x+tanx-1=0
4.
Prove that
tan2 α −1+ cos2 α = tan2 α sin2 α
tan
2
a-1+cos
2
a=tan
2
asin
2
a
5.
Prove that
tanβsinβ + cosβ = secβ
tanbsinb+cosb=secb
6.
Prove that
tanλcos2 λ +sin2 λ sinλ
= cosλ +sinλ
tanlcos
2
l+sin
2
l
sinl
=cosl+sinl
7.
Prove that
1+ tanθ 1− tanθ
= sec2θ + 2tanθ 1− tan2θ
1+tanq
1-tanq
=
sec
2
q+2tanq
1-tan
2
q
8.
Prove that
sin2 ω − cos2 ω tanω sinω + cosω tanω
= cosω − cotω cosω
sin
2
w-cos
2
w
tanwsinw+coswtanw
=cosw-cotwcosw
9.
Find a counterexample to show that the equation
secα − cosα = sinα secα
seca-cosa=sinaseca
is not an identity.10.
Write
tan π 4 − β⎛
⎝⎜ ⎞ ⎠⎟
tan
p
4
-b
æ
è
ç
ö
ø
÷
as a function of
β
b
only.11.
Write
cos λ + π 3
⎛ ⎝⎜
⎞ ⎠⎟
cosl+
p
3
æ
è
ç
ö
ø
÷
as a function of
λ
l
only.12.
Write
cos −83º( )
cos-83º
()
as a function of a positive angle.13.
Write
sin 125º( )
sin125º
()
in terms of its co-function. Make sure your answer is a function of a positive angle.14.
Find the exact value of
sin 195º( )
sin195º
()
15.
Sketch a graph of
y = sin −2x( )
y=sin-2x
()
, paying particular attention to the critical points.16.
If
cot2θ = 5 12
cot2q=
5
12
, with
0 ≤ 2θ ≤ π
0£2q£p
, find
cosθ, sinθ,
cosq,sinq,
and
tanθ
tanq
.17.
Find the exact value of
sin2α
sin2a
if
cosα = 4 5
cosa=
4
5
(α in Quadrant I).18.
Find the exact value of
tan2β
tan2b
if
sinβ = 5 13
sinb=
5
13
(
β
b
in Quadrant II)19.
Solve
sin2x +sinx = 0
sin2x+sinx=0
for 0 ≤ x ≤ 2π20.
Write
2sin37ºsin26º
2sin37ºsin26º
as a sum (or difference).
