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