Download ( 471- a) cot = b) (sin 0)2 = sin2 0 c) cos-11= 0 d) csc— r = sec

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Honors Pre-Calculus: Chapter 4 Practice Test (1)
1. Indicate whether each is True or False.
a) cot
( 471-
b) (sin 0)2 = sin2 0
=
3I
571.
r
d) csc— = sec12
12
c) cos-1 1= 0
e)
< 0 < 37z- —> cos 0 < 0
g) — sin —
71- = sin
2
i) tan
2
2r
2r
=sec
1
7
7
f,) cot 0 =
csc
sec q$
h) For r <0 < 37r , tan 0 = tan (0— ).
2
j) cos(-15°) =
1
sec15°
371.
k) If cos 0 > 0 and sin 0 < 0 , then — < 0 <2r .
2
2. Evaluate the other five trigonometric functions of 0 if sec 0 = —3.5 and csc 0 > 0.
3
I.
7
3. Let f(0) =TRIG 0 where TRIG can be replaced by any of the six trigonometric functions. Which
function(s) could replace TRIG in each situation?
(
r
47r \
b) f
a) f — =1
=-f
3 )
4)
tOkn
C.,
c) f
y
(2) =
C
d) f (0)> 0 for
5
(
A
C
e) f (0) = f (0 —2g)
f) The domain of f(0) is (—G0,09).
I'
A
JI
g) f (0 +37r) = f (0)
h) —2f
6)
I\
(
0
71.
f(0) = co-f --
j) f(0) =
, where co-f is the cofunction of f.
1
, where co-f is the cofunction of f .
cof (0)
f
( 67T
4
II
4. Verify.
a)
1
- sec 0 + tan 0
sec 0 - tan 0
1
2
b) (sec - tan 0) -
sin
1+ sin 0
1 -
f - 7-
-\\
-
421/
3
c)
1 + sin x
cos x
1 1-
cos x
= 2sec x
.
l+sinx
•Y, AY .4-6)
'
0—c
7
,K
d)
sin 0 (csc - sin 0)
= sec 2 0
ro<
V\ X '1
.1"
e)
1
1
= 2 sec2
+
1-sin01+sin0
f) csc4 0 - csc2 0 = cot4 0 + cot2 0
c5(z
6) t)(9-k
-
tA
5. Let f (x) = x3 — 7r 2x and g (x) = sin x . Show that all the zeros of f are also zeros of g.
0
2x 2—10x +12
6. Identify all asymptotes and intercepts of the rational function f (x) — 3
X — 1 OX 2 — 24x
0
1,1
V
1(A.
O
a
( V .-
0
() 0
0
I Act
f(-o)
uno ,i
7. Identify all asymptotes and intercepts on the interval [0,27r) of the trigonometric function
f (x) = tan x
8. From a point 150 ft in front of a building, the angles of elevation to the top of the building and to the
top of the flagpole atop the building are 42° and 47°, respectively. Draw a figure. Label the height
of the building and the flagpole with appropriate variables. Find the height of the flagpole to the
nearest tenth of a foot.
4
9. Explain why each of the following is not possible.
8
a) It is given that sin a = — and tan a =
10
4
5
b) It is given that cos p = - and tan
4
<0.
8
c) It is given that sin 0 = -- and the terminal side of0 lies in Quadrant II.
19
8
10. Given cos 0 = — , evaluate tan 0 using two methods.
17
a) Right triangle trigonometry
b) A Pythagorean identity
1/
11. Find all values of 6' on the interval [0,27r) such that cos 0 = 0.2725.
1, (796
z.
/7 C
12. Find all values of x on the interval [0,27r) such that csc x = —1.3784.
S
13. A tunnel for a highway is to be cut through a mountain, which is 14,411 feet high. At a distance of 2
miles from the base of the mountain, the angle of elevation to the summit is 36°. From a distance of
one and a half miles on the opposite side of the mountain, the angle of elevation is 47°. Find the
length of the tunnel to the nearest foot.
(-1 14
-cA .n366
t n-
MOP