check the attachment please i only need answers no solution,. Thank you
1-A point P(x, y) is shown on the unit circle U corresponding to a real number t. Find the
values of the trigonometric functions at t.
sin t =
cos t =
tan t =
csc t =
sec t =
cot t =
2-Let P(t) be the point on the unit circle U that corresponds to t. If P(t) has the given
rectangular coordinates, find the following.
?
3
5
,
4
5
(a) P(t + ?)
(x, y) =
(b) P(t ? ?)
(x, y) =
(c) P(?t)
(x, y) =
(d) P(?t ? ?)
(x, y) =
3-Let P be the point on the unit circle U that corresponds to t. Find the coordinates of P and
the exact values of the trigonometric functions of t, whenever possible. (If an answer is
undefined, enter UNDEFINED.)
(a) t = 5?/2
P(x, y)
=
sin(5?/2)
=
cos(5?/2) =
tan(5?/2) =
csc(5?/2) =
sec(5?/2) =
cot(5?/2)
=
(b)
t = ??/2
P(x, y)
=
sin(??/2)
=
cos(??/2) =
tan(??/2) =
csc(??/2) =
sec(??/2) =
cot(??/2)
=
4-Use a formula for negatives to find the exact value.
(a)
sin(?270?)
(b)
cos
?
3
?
4
(c)
tan(?45?)
5-Determine whether the equation is an identity for all values of x where the functions are
defined.
cos (?x) sec (?x) = ?tan x
Yes, it is an identity.
No, it is not an identity.
6-Complete the statement by referring to a graph of a trigonometric function.
(a)
As x ? (??/4), cot x ?
.
(b)
As x ? (?3?)?, cot x ?
.
7-Refer to the graph of
y = sin x or y = cos x
to find the exact values of x in the interval [0, 4?] that satisfy the equation. (Enter your
answers as a comma-separated list.)
cos x = 1
x =
8-Refer to the graph of
y = tan x
to find the exact values of x in the interval
(??/2, 3?/2)
that satisfy the equation. (Enter your answers as a comma-separated list.)
tan x = 0
x =
9-Find the reference angle ?R if ? has the given measure.
(a) 5?/4
?R =
(b)
?R =
2?/3
(c)
?5?/6
?R =
(d)
13?/4
?R =
10-Find the exact value.
(a) sin 240?
(b)
sin(?300?)
11-Approximate to three decimal places.
(a) sec 71?50'
(b)
csc 0.31
12-Approximate the acute angle ? to the following.
cos ? = 0.3620
(a) the nearest 0.01?
?
(b) the nearest 1'
?
'
13-Approximate to four decimal places.
(a) sin 83?40'
(b)
cos 514.7?
(c)
tan 3
(d)
cot 158?40'
(e)
sec 1016.1?
(f)
csc 0.42
14-Approximate, to the nearest 0.01 radian, all angles ? in the interval [0, 2?) that satisfy
the equation. (Enter your answers as a comma-separated list.)
(a)
sin ? = 0.4292
?=
(b)
cos ? = ?0.1403
?=
(c)
tan ? = ?3.2203
?=
(d)
cot ? = 2.6918
?=
(e)
sec ? = 1.7153
?=
(f)
csc ? = ?4.8729
?=
15-Find the amplitude and the period and sketch the graph of the equation.
(a)
y = 3 cos x
amplitude
period
(b)
y = cos 8x
amplitude
period
(c)
y=
1
4
cos x
amplitude
period
(d)
y = cos
1
6
amplitude
period
x
(e)
y = 2 cos
1
6
x
amplitude
period
(f)
y=
1
4
amplitude
period
cos 4x
(g)
y = ?2 cos x
amplitude
period
(h)
y = cos(?6x)
amplitude
period
16-Find the amplitude, the period, and the phase shift.
y = 4 sin 3?x
amplitude
period
phase shift
Sketch the graph of the equation.
17-Find the amplitude, the period, and the phase shift.
y = ?4 cos
2x +
?
3
amplitude
period
phase shift
Sketch the graph of the equation.
18-The graph of a sine function with a positive coefficient is shown in the figure.
(a) Find the amplitude, period, and phase shift. (The phase shift is the first negative zero that
occurs before a maximum.)
amplitude
period
phase shift
(b) Write the equation in the form y = a sin(bx + c) for a > 0, b > 0, and the least positive
real number c.
19-Find the period.
y=
1
6
tan
4x ?
?
7
Sketch the graph of the equation. Show the asymptotes.
20-Find the period.
y = 6 sec
6x ?
?
6
Sketch the graph of the equation. Show the asymptotes.
21-Use the graph of a trigonometric function to aid in sketching the graph of the equation
without plotting points.
y = 9|sin x| + 10