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
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)
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
(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 &gt; 0, b &gt; 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