Question

http://prntscr.com/nrf7dj

Answer 1

@Narad

Answer 2

The domain of
\[y=sinx\]
is all real numbers
\[D _{f} = \mathbb{R} \]

Answer 3

http://prntscr.com/nrfalb

Answer 4

Since
\[-1\le sinx \le 1\]
The range is
\[-1 \le y \le1\]

Answer 5

http://prntscr.com/nrfcj3

Answer 6

The domain of the function
\[y=cosx\]
is all real numbers
\[D _{f} = \mathbb{R} \]

Answer 7

http://prntscr.com/nrfebc

Answer 8

Since the domain of
\[y=tanx\]
is\[x \in (-\pi/2, \pi/2)\]
The range is
\[y \in \mathbb{R} \]
that is , all real numbers

Answer 9

okay

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Answer 10

When
\[x=0\]
\[f(0)=\ 0.5tan0=0\]
This is not the case in the graph
Therefore,
The answer is FALSE

Answer 11

Got it

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Answer 12

Since the graph passes through the origin,

The first, second and fourth options are not correct

\[y= 2tanx\]

When \[x=\pi/4\]

\[y=2\] from the graph

The correct option is option C

Answer 13

Okay

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Answer 14

Since the range is
\[-1\le y \le 1\]
You can remove option D

\[f(x)=2sinx\]

Also you can remove
\[f(x)=sinx+2\]
for the same reasons
With respect to the graph of
\[f(x)=sinx\]
This graph has been shifted to the right by
\[\pi/4\]
The answer is option A
\[f(x)=\sin(x-45)\]

Answer 15

Okay

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Answer 16

When \[x=0\]
\[f(0)=\sin(0-180)-1=\sin(-180)-1=0-1=-1\]
This point lies on the curve
When
\[x=0.5\pi\]
\[f(0.5\pi)=\sin(90-180)-1=\sin(-90)-1=-1-1=-2\]
This point also lies on the curve
when
\[x=-0.5\pi\]
\[f(-0.5\pi)=\sin(-90-180)-1=\sin(-270)-1=1-1=0\]
This point is on the curve
We can, therefore, conclude that
\[f(x)=\sin(x-180)-1\]
is the equation of the graph
This is TRUE

Answer 17

Okay

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Answer 18

When\[x=0\]
\[f(0)=\cos0-3=1-3=-2\]
This point does not lie on the curve
When \[x=\pi/2\]
\[f(\pi/2)=\cos(\pi/2)-3=0-3=-3\]
This point does not lie on the curve

We can conclude that the equation of the graph is not
\[f(x)=cosx-3\]
The answer is FALSE

Answer 19

okay

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Answer 20

The following points lie on the curve
\[(0,0)\]
\[(\pi/2,1)\]
\[(-\pi/2,-1)\]
The domain is \[\mathbb{R} \] and
the range is
\[-1\le f(x)\le1\]
This function is
\[f(x)=sinx\]
THe answer is option B

Answer 21

Okay
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Answer 22

The cosine of an angle is by definition
\[\cos=\]
(adjacent)/(hypotenuse)
In the triangle ABC
\[cosB=BC/AB=a/c\]
You can reject the first three options
The correct answer is option D

Answer 23

okay

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Answer 24

The tangent of an angle is by definition
\[\tan\]
=(opposite)/(adjacent)
Therefore,
in the triangle ABC
\[tanA=BC/AC= a/b\]
You can reject the first 3 options and accept option D

Answer 25

Got it

http://prntscr.com/nrg85a

Answer 26

By definition, \[sine\]
of an angle is
=(opposite)/(hypotenuse)

Here, in the triangle ABC

\[\sin B=AC/AB=5/13\]
You can accept the first option and reject the others

Answer 27

Okay

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Answer 28

The tangent of an angle is

tan=(opposite)/(adjacent)
Here in the triangle ABC
\[\tan B=AC/BC=9/12=3/4\]
The answer is option C

Answer 29

Okay

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Answer 30

The secant of an angle is

secant = (hypotenuse)/(adjacent)

Here, in the triangle ABC
\[secA= AB/AC=13/5\]

You can accept the first option and reject the others

Answer 31

Okay

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Answer 32

The sine of an angle is by definition

sine=(opposite)/(hypotenuse)

Therefore, in the triangle ABC

\[sinA=BC/AB=12/15=4/5\]

You can accept the third option C

Answer 33

Okay

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Answer 34

Question nº19
\[cosA=0.34\]
Therefore,
\[A = \cos ^{^-1} 0.34\]
From my calculator,
\[A= 70.12º\]
The answer is option B

Answer 35

Question nº20

\[sinB=0.45\]

Therefore,
\ From my calculator, \ The correct answer is option D

Answer 36

Okay

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Answer 37

Something went wrong in the last answer, can you read everything

Answer 38

Maybe its 47?

Answer 39

The cosine of an angle is by definition

cosine=(adjacent)/(hypotenuse)

Therefore,

In the triangle ABC

cos40º=AC/AB = AC/3

therefore,

AC=3*cos40º= 2.30 cm

Answer 40

I'll rewrite question nº20
sinB=0.45

B=arcsinB=arcsin(0.45)

From my calculator

B=0.47
The answer is option D

Answer 41

http://prntscr.com/nrl8fe

Answer 42

@Narad

Answer 43

The tangent og an angle is defined as

tangent=(opposite)/(adjacent)

Apply this to the triangle ABC

tanA=BC/AC

BC=AC*tanA=29.3*tan28º =15.58 mi

Answer 44

Got it

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Answer 45

Since the triangle is right angled and the sum of the angles of a triangle is =180º

B+28º=90º

B=90-28=62º

Answer 46

Okay

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Answer 47

The altitude = height of the plane = 8 mi

The distance to the runaway (hypotenuse)= 175 mi

The sine of an angle is

sine=(opposite)/(hypotenuse)

sin(angle)=8/175=0.046

The angle is = 2.62º

Answer 48

http://prntscr.com/nrlc5i

Answer 49

Since the triangle is a right angled isoceles triangle (45º,45º,90º)

The height above 6feet is=60feet

The height of the building is =60+6=66ft

Answer 50

okay

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Answer 51

We have already done this question

f(0)=0

f(pi/2)=1

f(-pi/2)=-1

The equation of the graph is

f(x)=sinx

The correct option is B

Answer 52

Okay

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Answer 53

The points are

f(pi/4)=0

f(3/4pi)=1

f(-pi/4)=-1

and the range is

y = [-1, 1]

The equation of the graph is a sine function which has been translated to the right by pi/4

Therefore,

f(x)=sin(x-45º)

or

f(x)=sin(x-pi/4)

Answer 54

http://prntscr.com/nrmdy9

Answer 55

The domain of the graph is All Real Numbers

The range of the graph is

= [-2, 2] = 2* [-1, 1]

The values taken by the graph are

f(0)=0

f(-pi/2)=-2

f(pi/2)= 2

The equation of the graph is

y=2sinx

Answer 56

http://prntscr.com/nrw8xh

Answer 57

Question nº29

The range of

y=tanx

is All Real Numbers

Therefore,

The range of

y=tanx+2

is also All Real Numbers

Answer 58

Question nº30

The range of y=sinx is

\[-1 \le sinx \le 1\]

The range of y=2sinx is

\[-2 \le 2sinx \le 2\]

The range of y=2sinx +1 is

\[-1 \le 2sinx +1 \le 3\]

The answer is

\[y \in [-1, 3]\]

Answer 59

http://prntscr.com/nrwdxp

Answer 60

Question nº31

180º is equivalent to \[\pi\] radians

Therefore,

125º is equal to \[\pi/180*125 rad\]

\[=25/36\pi\]

The answer is the last option, option D

Answer 61

Question nº32

\[\pi\] radians is equivalent to 180º

Therefore,

3.6 radians is equivalent to

\[180/\pi*3.6\]
\[= 206.3 º\]

The answer is the first option, option A

Answer 62

okay

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Answer 63

Question nº33

180º is equivalent to \[\pi rad\]

Therefore,

135º is equivalent to
\[\pi/180*135= 3/4\pi\]
The answer is \[=3/4\pi\]

Answer 64

Question nº34

Let's first convert 150º into radians

The conversion is

\[150º=\pi/180*150 = 5/6\pi\]

Therefore,

The cosine of 150º, according to the unit circle is
\[\cos150º =-\cos30º =-\sqrt3/2\]

Answer 65

okay

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Answer 66

Question nº 35

The cosine of the angle is
\[cosA =-0.45\]

This means that the angle is in 2nd Quadrant or 3rd Quadrant

Therefore
\[A=\cos ^{-1} (-0.45) =2.04rad = 116.74º\]
Here the answer is in the 2nd Quadrant

Answer 67

Question nº 36

The current is dragging you downstream

Therefore,
\[\tan 25º = 375/d\]

So,

\[d=375/\tan25º = 804.2ft\]
The distance downstream is = 804.2 ft

Answer 68

Okay

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Answer 69

The domain is

\[x \in \mathbb{R} \]

The range is
\[y \in [-1, 1]\]

Particulars values are

\[f(0)=0\]

\[f(\pi/2)=1\]
and \[f(-\pi/2)=-1\]

The equation of the graph is
\[y=sinx\]

Answer 70

okay

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Answer 71

The domain is
\[ x \in \]

The range is
\[ y \in [-1, 5]\]

Particular values are

\[f(0)=2\]
\[f(\pi/2)=5\]
and
\[f(-\pi/2)=-1\]

This is a sinusoidal function

\[y = 3sinx +2\]
The equation of the graph is
\[y=3sinx+2\]

Answer 72

Domain is \[x \in \mathbb{R} \]

Answer 73

Okay and last one:

http://prntscr.com/nrwy5q

Answer 74

The range of sinx is

\[-1\le sinx \le 1\]
so,
\[-3 \le 3sinx \le3\]

And
\[0 \le 3sinx+3 \le 6\]
The range of the function\[y = 3sinx+3\]
is
\[y \in [0, 6]\]

Answer 75

Thank you!

Answer 76

You are welcome