Hey, I need help with this questions please, they are quite easy, but there are so many of them

.

–/1 pointsSPreCalc7 6.3.002.

My NotesAsk Your Teacher

The sign of a trigonometric function of θ depends on the —Select—axisquadrant in/on which the terminal side of the angle lies.In Quadrant II, sin(θ) is —Select—positivenegative .

In Quadrant III, cos(θ) is —Select—positivenegative .

In Quadrant IV, tan(θ) is —Select—positivenegative .

2.

–/1 pointsSPreCalc7 6.3.003.

My NotesAsk Your Teacher

(a) If θ is in standard position, then the reference angle θ

is the acute angle formed by the terminal side of θ and the —Select—x-axisy-axis . So the reference angle for

θ = 110°

is

θ = °,

and that for

θ = 190°

is

θ = °.

(b) If θ is any angle, the value of a trigonometric function of θ is the same, except possibly for sign, as the value of the trigonometric function of

θ.

So

sin(110°) = sin

°

, and

sin(190°) = −sin

°

.

3.

–/1 pointsSPreCalc7 6.3.007.

My NotesAsk Your Teacher

Find the reference angle for the given angle.(a)265°
°

(b)820°

°

(c) −95°

°

4.

–/1 pointsSPreCalc7 6.3.011.

My NotesAsk Your Teacher

Find the reference angle for the given angle.(a)

3π

5

(b)

−0.8π

(c)

0.8

5.

–/1 pointsSPreCalc7 6.3.015.

My NotesAsk Your Teacher

Find the exact value of the trigonometric function. (If an answer is undefined, enter UNDEFINED.)tan(150°)

6.

–/1 pointsSPreCalc7 6.3.018.

My NotesAsk Your Teacher

Find the exact value of the trigonometric function. (If an answer is undefined, enter UNDEFINED.)csc(240°)

7.

–/1 pointsSPreCalc7 6.3.025.

My NotesAsk Your Teacher

Find the exact value of the trigonometric function. (If an answer is undefined, enter UNDEFINED.)sin

3π

2

8.

–/1 pointsSPreCalc7 6.3.029.

My NotesAsk Your Teacher

Find the exact value of the trigonometric function. (If an answer is undefined, enter UNDEFINED.)csc

−

π

6

9.

–/1 pointsSPreCalc7 6.3.034.

My NotesAsk Your Teacher

Find the exact value of the trigonometric function. (If an answer is undefined, enter UNDEFINED.)cos

3π

4

10.

–/1 pointsSPreCalc7 6.3.039.

My NotesAsk Your Teacher

Find the quadrant in which θ lies from the information given.sec(θ) < 0 and tan(θ) < 0

III IIIIV

11.

–/1 pointsSPreCalc7 6.3.041.

My NotesAsk Your Teacher

Write the first trigonometric function in terms of the second for θ in the given quadrant.tan(θ), cos(θ); θ in Quadrant III

tan(θ) =

12.

–/1 pointsSPreCalc7 6.3.043.

My NotesAsk Your Teacher

Write the first trigonometric function in terms of the second for θ in the given quadrant.cos(θ), sin(θ); θ in Quadrant IV

cos(θ) =

13.

–/1 pointsSPreCalc7 6.3.049.

My NotesAsk Your Teacher

Find the values of the trigonometric functions of θ from the information given.cos(θ) =

4

19

, sin(θ) < 0

sin(θ)	=
tan(θ)	=
csc(θ)	=
sec(θ)	=
cot(θ)	=

14.

–/1 pointsSPreCalc7 6.3.051.

My NotesAsk Your Teacher

Find the values of the trigonometric functions of θ from the information given.csc(θ) = 4,

θ in Quadrant I

sin(θ)	=
cos(θ)	=
tan(θ)	=
sec(θ)	=
cot(θ)	=

15.

–/1 pointsSPreCalc7 6.3.056.

My NotesAsk Your Teacher

If θ = π/4,

find the value of each expression. (Round your answers to three decimal places, if necessary.)

sin2(θ)	=
sin(θ2)	=

16.

–/1 pointsSPreCalc7 6.3.058.

My NotesAsk Your Teacher

Find the area of a triangle with the given description. (Round your answer to one decimal place.)a triangle with sides of length 12 and 23 and included angle 20°

17.

–/1 pointsSPreCalc7 6.3.059.MI.

My NotesAsk Your Teacher

Find the area of the triangle with the given description. (Round your answer to one decimal place.)an equilateral triangle with side of length 14

18.

–/1 pointsSPreCalc7 6.3.063.

My NotesAsk Your Teacher

Find the area of the shaded region in the figure. (Round your answer to two decimal places.)

19.

–/1 pointsSPreCalc7 6.3.067.

My NotesAsk Your Teacher

A graphing calculator is recommended.

A rectangular beam is to be cut from a cylindrical log of diameter d = 22 cm. The figures show different ways this can be done.

(a) Express the cross-sectional area of the beam as a function of the angle θ in the figures.
A(θ) =

(b) Graph the function you found in part (a).

(c) Find the dimensions of the beam with largest cross-sectional area. (Round your answers to two decimal places.)

width	cm
depth	cm

20.

–/1 pointsSPreCalc7 6.3.068.

My NotesAsk Your Teacher

The strength of a beam is proportional to the width and the square of the depth. A beam is cut from a cylindrical log of diameter d = 20 cm. The figures show different ways this can be done. Express the strength of the beam as a function of the angle θ in the figures. (Use k as your proportionality constant.)
S(θ) =

If we know the values of sin(x) and cos(x),

we can find the value of

sin(2x)

by using the —Select—Half-AngleDouble-Angle Formula for Sine.

State the formula:

sin(2x) =

.

2.

–/1 pointsSPreCalc7 7.3.002.

My NotesAsk Your Teacher

If we know the value of cos(x)

and the quadrant in which

x/2

lies, we can find the value of

sin(x/2)