Download Trigonometry Test 13 Use the double angle identities to find sin, cos

Trigonometry Test 13
Use the double angle identities to find sin, cos and tan of each.
1 - 2) Find t, given cos 2t = 
1
with t in quadrant 3.
9
Use Cos 2t = 2 cos2 t – 1
Sin 2t = 2 Sin t Cos t

3 - 4) Find 2t, given cos t = 
1
with t in quadrant 2.
4
Use the above equation.

Use the
1
angle identities to find sin, cos and tan.
2
5 - 6) A = 67.5

Cos
1 Cos A
A
Sin
= 
2
 2
1 Cos A
A
Tan
=
Sin A
2





1
Find each of the following. Use the angle identities.
2
7) sin A, given cos 2A = 
1 Cos A
A
= 
2
2
5
, A is in quadrant 2.
12


Are the following one-to-one? If yes, find the inverse function's equation.
8) 2x + 3y = 6
9) x + 5 =
3
y
Determine if they are inverses of each other. Show your work.
10)
f(x) = -2x + 1,
g(x) =

x  1
2
For each of the following give the value of y using the table.
11) y = Arcsin
2
2
11a) y = Arccot 

3
3
12) y = Arcsin 1
12a) y = Arccsc (-2)

Find the value of y.
12
)
5
13) y = Cos(Arccot
3
14) y = Tan(Arcsin  )
5
Solve for x.Use the table to find all possible angles. ( 
3 pts. each) 0 ≤ x < 360
15) 3 Tan x + 5 = 2
17) Cos2 x + 2 Cos x + 1 = 0
20) Find the area of this triangle. a = 22, b = 45, c = 29
18) 3 Sin2 x - Sin x - 2 = 0
(3 pts.)
Area =
1
(a + b + c)
2
s(s  a)(s  b)(s  c)
s=

Use the Law of Sines to find all missing sides and angles. 
( 5 pts.)
a
b
c


Sin A Sin B Sin C
21 - 23) <B = 52  , <C = 29  , a = 4



Use the Law of Cosines and then the Law of Sines to find the sides and angles. (5 pts)
23a - 25) <A = 42.3  , b = 12.9, c = 15.4

a2= b2 + c2 – b• c• Cos A