Redwood High School. Department of Mathematics
2016-2017 Honors Adv. Alg. Test S2 #6
Student waiting for Spring break:___________________________________
Please work this problems in your notebook
Simplify and complete the indentity
1) csc x(sin x + cos x) = ?
2) sec x -
3)
12) -tan 2 x + sec 2 x = sec 2 x cos 2 x
1
=?
sec x
13)
tan t
1 + cot t tan2 t + 2 - csc2 t
+
=
1 - cot t
tan t
tan t - 1
Simplify and complete the indentity
sin x cos x
+
=?
cos x sin x
14) Graph the following function: Y=1 -
sin2 x
1 + cos x
4) 2 tan x - (1 + tan x)2 = ?
5)
(cot x + 1)(cot x + 1) - csc2 x
=?
cot x
Simplify the expression and then graph
6) Graph the following function: Y=
1 - sin2 x
sin x - csc x
Simplify the expression and then graph
15) Graph the following function: Y=
Determine if the following is an identity.
7) 1 + sec2 x sin2 x = sec2 x
8)
1 + csc x
= cos x + cot x
sec x
9) tan2 x = sec2 x - sin2 x - cos2 x
10)
cot x
csc x - 1
=
1 + csc x
cot x
11)
cot 2 x
1 - sin x
=
csc x + 1
sin x
1
sin2 x - 1
cos (x)
Graph
19) Graph the following function: Y=
16) Graph the following function:
(sin + cos )2
Y=
1 + 2 sin cos
17) Graph the following function:
Y=tan (cot - cos )
18) Graph the following function:
sec sin
Y=
-1
tan
2
sin2 - 1
sin + 1
Answer Key
Testname: HADVALG S2 TEST #8 TRIG II V1SHORT.0
1) 1 + cot x
2) sin x tan x
3) sec x csc x
4) - sec2 x
5) 2
6) -sin x
sin2 x
= 1 + tan2 x = sec2 x.
7) 1 + sec2 x sin2 x = 1 +
cos2 x
8)
1 + csc x
1
cos x (sin x + 1) cos x sin x cos x
= cos x 1 +
=
=
+
= cos x + cot x.
sec x
sin x
sinx
sin x
sin x
9) tan2 x = sec2 x - 1 = sec2 x - (sin2 x + cos2 x) = sec2 x - sin2 x - cos2 x.
cot x
cot x cot x
csc 2 x - 1
(csc x + 1)(csc x - 1) csc x - 1
=
=
=
=
.
10)
1 + csc x (1+ csc x) cot x (1+ csc x) cot x
(1+ csc x) cot x
cot x
11)
cot 2 x
csc2 x - 1 (csc x + 1)(csc x - 1)
1
sin x 1 - sin x
=
=
= csc x - 1 =
=
.
csc x + 1
csc x + 1
csc x + 1
sin x sin x
sin x
sin 2 x
1
1
+
=
(-sin 2 x + 1) = sec 2 x cos 2 x.
12) -tan 2 x + sec 2 x = 2
2
cos x cos x cos 2 x
13)
tan t
1 + cot t tan2 t + 1 - cot2 t tan 2 t + 1 + 1 - csc2 t tan2 t + 2 - csc2 t
+
=
=
=
.
1 - cot t
tan t
tan t (1 - cot t)
tan t - 1
tan t - 1
14)
15)
16)
17)
18)
19)
cos x
-cos x
1
1 - sin
0
sin - 1
3