Trig ch 6

Question 1

How to find the value of cosec, sec and cot?

Answer 1

1/Cosx,secx, cot.

Work out the value on the sin, cos and tan and do the reciprocal of that value.

Question 2

What does the cosec curve look like?

Answer 2

inverted parabola which intersects sin graph at max and min points.

Asymptotes beside where the U’s level off (asymptote every 180*)

Question 3

What does the sec curve look like?

Answer 3

asymptotes at 90* and 270*.

n shaped parabola at minimum of cos graph.

Half parabolas either side of the asymptotes at 90 and 270.

Question 4

What are two differences between sec and cosec curve?

Answer 4

In cosec asymptotes are every 180* (180,360), whilst in sec asymptotes are every 180* (90,270).

In cosec, there is a U and an n.
In sec, there is an l, n and l shape.

Question 5

How do you know where the asymptotes will be on reciprocal curves?

Answer 5

Where the sin/cos/tan x=0 as this will cause the reciprocal curve to be 1/0 which is undefined and needs asymptote.

Question 6

Why do the reciprocal trig curves have the shapes they take?

Answer 6

Because as the decimal values of the original trig graph gets smaller the larger the reciprocal graph gets.
It then gets to 0 which causes it to be undefined and have an asymptote.

Question 7

What does the cot graph look like?

Answer 7

Reflected tan graph, asymptotes stay in the same place.

Question 8

What are the maxima/ minima and asymptotes for cot graph?

Answer 8

asymptotes at 180 and 360 then negative cubics in between these asymptotes.

Question 9

How to solve equations involving sec, cosec and cot

Answer 9

Convert them to expressions in times of sin, cos and tan

Question 10

What is the domain and range of sec graph?

Answer 10

Domain = x is all real numbers but x cannot equal 180n-90.
Range = f(x) is greater than of equaled to 1 and f(x) is less than -1

Question 11

What is the domain and range of cosec graph?

Answer 11

Domain = x is all real values and not equal to 180n
Range = f(x) greater than or equal to 1 and f(x) is less than or equaled to 1.

Question 12

What is the domain and range of cosec graph?

Answer 12

Domain = x is all real values not equal to 180n
Range g(x) is all real values.

Question 13

What is the domain and range of the cot graph?

Answer 13

Domain= x is all real values except from 180n
Range= f(x) is all real values

Question 14

why would cos^3x=8 have no solutions?

Answer 14

once you cube root cos^2x=+-2

As cos graph has max at 1 and min at -1 there can be no solutions.

Question 15

What to do when solving when there is a 2x inside the angle?

Answer 15

• Change the range by multiplying by 2.
• Find all the solutions in this range.
• Then divide all the solutions by 2 and see which ones fit the initial range.

Question 16

How to solve trig equations involving reciprocal trig?

Answer 16

• make it 1/sin/cos/tan
• then using denominator rule switch it with value
• do the inverse to find the first angle
• check if the value of y is positive or negative
• find all solutions for given interval

Question 17

How to solve equations that are in a negative range?

Answer 17

Go in an anti clockwise direction and check whether you would continue to add negative or add positive.

Question 18

How large is an obtuse angle?

Answer 18

Between 90. and 180

Question 19

How large is a reflex angle?

Answer 19

Between 180* and 360*

Question 20

How large is an acute angle?

Answer 20

Less than 90*

Question 21

How to workout a question that is like given that tana is x/y what is seca?

What is important about these questions?

Answer 21

Draw out triangle to find the value of the reciprocal of the one you want to find out.

They will tell you the angle is obtuse, reflex or acute so you must draw out cast and find out what the angle will be in the given quadrant.

Question 22

How do you derive the two other Pythagorean identities from Sin^2+Cos^2=1

What is the difference between them?

Answer 22

To get the tan^2+1=sec^2 divide through by cos^2.

To get cos^2+1=cosec^2 divide through by sin^2 as you want to have a cos/sin which is the same as cot.

you divide one by cos^2 and divide the other by sin^2

Question 23

What are the inverse functions of sin, cos and tan?

Answer 23

Arcsin
Arcos
Arctan

Question 24

How does the rule of functions link to the inverse trig functions

Answer 24

The inverse of the trig functions which would become one-many which is not a function.

Question 25

What is the condition on finding the inverse of sin cos and tan

Answer 25

You must restrict the theta values to when the sin, cos, tan is not many to one.

Question 26

In what line is the reflection of an inverse function done in?

Answer 26

Reflected in the line y=x

Question 27

How do the domain and range of trig and arc trig relate?

Answer 27

The domain of trig becomes the range of arctrig

The range of trig becomes the domain of arctrig

Question 28

How do you sketch the arctrig functions?

Answer 28

You swap the x and y coordinates of the original trig function.

Question 29

What is the domain and range of sin and arcsin.

Answer 29

Sin :Domain (-Pi/2 to Pi/2) Range (-1 to 1).

Arc sin: Domain (-1 to 1) Range (-Pi/2 to Pi/2)

Question 30

What is the domain and range of cos and arccos.

Answer 30

Cos: Domain (0 to Pi) Range (-1 to 1)
Arcos: Domain (-1 to 1) Range (0 to PI)

Question 31

Why do the domains and ranges of arctrig functions have to be restricted?

Answer 31

Because the trig curves are not many to one in these values.
Therefore, the inverse can be a function.

Question 32

What is the domain of range of tran and arc tan?

What is unique about tan in this instance?

Answer 32

Tan: Domain (-Pi/2 to Pi/2) Range : all real values
Arctan: Domain: all real values Range: (-pi//2 to pi/2).

The vertical asymptotes of tan at -pi/2 and pi/2 become horizontal asymptotes at this location.