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Math 30 > U3 A2 > Flashcards

U3 A2 Flashcards

1
Q

With an identity there are an ______ number of x values that will make that statement _____

A

Infinite

True

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2
Q

With an identity the left side will ALWAYS equal the ____ ____

A

Right side

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3
Q

An identity is a ____

A

Proof

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4
Q

What are the 4 basic identities

A

sin, cos, tan ratios, and

x^2 + y^2 = r^2

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5
Q

What are the restrictions on

tan theta= sin theta/cos theta

(And why)

A

Theta = 90 degrees + n(Pi), n€I

Since cos theta is in the denominator it cannot equal 0

Cos is the x coordinate on the unit circle and it has a 0 value at the two y intercepts

So starting at 90 degrees and every 180 degrees after that it equals 0

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6
Q

What are the two quotient identities

A

Tan theta = sin theta/ cos theta

cot theta= cos theta/ sin theta

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7
Q

What does simplifying trig expressions mean

A

Reducing the expression

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8
Q

Always try to put expressions in terms of____ and ____ when possible

A

Sin

Cos

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9
Q

If you’re multiplying a trig fraction by a whole number what should you do

A

Move the whole number to the numerator (makes it easier)

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10
Q

An identity is a ____ that requires you to show that the left side of the equation is ___ to the _____ side.

A

Proof

Equal

Right

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11
Q

Some identities cannot be proven for certain values of ____. These would be any _____ on the trigonometric ratio or expression.

A

Theta

Restrictions

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12
Q

What is one thing you can try when you get stuck proving/simplifying identities

A

Difference of squares for Pythagorean identities

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13
Q

What are the negative versions of sin^2+ cos^2 = 1

A
  • sin^2 = cos^2 - 1

- cos^2 = sin^2 - 1

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14
Q

What is the negative version of

tan^2 = sec^2 - 1

A

-tan^2 = 1- sec^2

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15
Q

What is the negative version of

cot^2 = csc^2 - 1

A

-cot^2 = 1-csc^2

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16
Q

Can you use your calc to prove or disprove an identity

And how

A

Yes

left side= y1
right side= y2

If you get the same graph it’s an identity

Degree or radian mode?

17
Q

What are the restrictions on
tan x

(And do you always have to list it even if it’s not in the denominator)

A

x = 90 degrees + n(Pi)

YES

18
Q

What are the restrictions on
cot x

(And do you always have to list it even if it’s not in the denominator)

A

x = n(Pi)

Idk

19
Q

What are the restrictions on
csc x

(And do you always have to list it even if it’s not in the denominator)

A

x = n(Pi)

Idk

20
Q

What are the restrictions on
sec x

(And do you always have to list it even if it’s not in the denominator)

A

x = 90 degrees+ n(Pi)

Idk

21
Q

WHAT DO YOU ALWAYS HAVE TO DO WHEN PROVING IDENTITIES TO CHECK ANSWER

A

GRAPH AND SEE IF THE TWO GRAPHS MATCH UP

22
Q

Sin(A + B) is this possible to distribute

And why

A

No

Sin is a ratio and a ratio needs an angle

23
Q

Steps for finding the exact ratio for sin15

A

1) expand angle into sin or diff statement
sin(45-30)

2) identify corresponding identity
3) make substitution
4) evaluate

24
Q

What is the solution to

root 6 - root 2

(And why)

A

root 6 - root 2

They’re unlike terms so you can’t add/subtract them

25
Q

What is the exact ratio of
tan270 degrees

(And why)

A

UNDEFINED

Tan= sin/cos

Cos is 0 at 270 degrees (x value)

So tan is undefined

26
Q

Sin and difference identities can be used to find the exact value of non special _____ by re writting it as a sim or difference of two _____ angles

A

Angles

Special

27
Q

Does cos2 theta = 2cos theta

A

No

28
Q

What does “a single trig ratio” mean

A

Can only have 1 ratio

29
Q

The invoice the positive ratio is the ___ _____

A

Reference angle

30
Q

Solving trig equations: if you take the inverse of the positive ratio and you get an error message what does this mean

A

Either the opposite or adjacent side is larger than the hypotenuse

(Can figure this out through the corresponding trig ratio)

31
Q

When you’re solving angles what mode should calc be in

A

Idk

32
Q

Solving trig equations: if you get an error message what is your answer

A

No roots

33
Q

Solving trig equations: why can’t you dive by a term that has a variable (Ex. cos x)

A

We would get rid of half of the solutions

34
Q

How to verify solutions when solving trig equations using identities

A

Use original equation

LS= y1

RS= y2

Points of intersection are solutions

35
Q

Steps for solving trig equations using identities

A

Fill in

36
Q

What’s the square root of 1

A

1

37
Q

What do you have to remember when labelling the unit circle

A

The angle is ALWAYS from the x axis so don’t mix up 30 degrees with 60 degrees in some quadrants

Math 30 (6 decks)

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