U3 A2 Flashcards
With an identity there are an ______ number of x values that will make that statement _____
Infinite
True
With an identity the left side will ALWAYS equal the ____ ____
Right side
An identity is a ____
Proof
What are the 4 basic identities
sin, cos, tan ratios, and
x^2 + y^2 = r^2
What are the restrictions on
tan theta= sin theta/cos theta
(And why)
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
What are the two quotient identities
Tan theta = sin theta/ cos theta
cot theta= cos theta/ sin theta
What does simplifying trig expressions mean
Reducing the expression
Always try to put expressions in terms of____ and ____ when possible
Sin
Cos
If you’re multiplying a trig fraction by a whole number what should you do
Move the whole number to the numerator (makes it easier)
An identity is a ____ that requires you to show that the left side of the equation is ___ to the _____ side.
Proof
Equal
Right
Some identities cannot be proven for certain values of ____. These would be any _____ on the trigonometric ratio or expression.
Theta
Restrictions
What is one thing you can try when you get stuck proving/simplifying identities
Difference of squares for Pythagorean identities
What are the negative versions of sin^2+ cos^2 = 1
- sin^2 = cos^2 - 1
- cos^2 = sin^2 - 1
What is the negative version of
tan^2 = sec^2 - 1
-tan^2 = 1- sec^2
What is the negative version of
cot^2 = csc^2 - 1
-cot^2 = 1-csc^2
Can you use your calc to prove or disprove an identity
And how
Yes
left side= y1
right side= y2
If you get the same graph it’s an identity
Degree or radian mode?
What are the restrictions on
tan x
(And do you always have to list it even if it’s not in the denominator)
x = 90 degrees + n(Pi)
YES
What are the restrictions on
cot x
(And do you always have to list it even if it’s not in the denominator)
x = n(Pi)
Idk
What are the restrictions on
csc x
(And do you always have to list it even if it’s not in the denominator)
x = n(Pi)
Idk
What are the restrictions on
sec x
(And do you always have to list it even if it’s not in the denominator)
x = 90 degrees+ n(Pi)
Idk
WHAT DO YOU ALWAYS HAVE TO DO WHEN PROVING IDENTITIES TO CHECK ANSWER
GRAPH AND SEE IF THE TWO GRAPHS MATCH UP
Sin(A + B) is this possible to distribute
And why
No
Sin is a ratio and a ratio needs an angle
Steps for finding the exact ratio for sin15
1) expand angle into sin or diff statement
sin(45-30)
2) identify corresponding identity
3) make substitution
4) evaluate
What is the solution to
root 6 - root 2
(And why)
root 6 - root 2
They’re unlike terms so you can’t add/subtract them
What is the exact ratio of
tan270 degrees
(And why)
UNDEFINED
Tan= sin/cos
Cos is 0 at 270 degrees (x value)
So tan is undefined
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
Angles
Special
Does cos2 theta = 2cos theta
No
What does “a single trig ratio” mean
Can only have 1 ratio
The invoice the positive ratio is the ___ _____
Reference angle
Solving trig equations: if you take the inverse of the positive ratio and you get an error message what does this mean
Either the opposite or adjacent side is larger than the hypotenuse
(Can figure this out through the corresponding trig ratio)
When you’re solving angles what mode should calc be in
Idk
Solving trig equations: if you get an error message what is your answer
No roots
Solving trig equations: why can’t you dive by a term that has a variable (Ex. cos x)
We would get rid of half of the solutions
How to verify solutions when solving trig equations using identities
Use original equation
LS= y1
RS= y2
Points of intersection are solutions
Steps for solving trig equations using identities
Fill in
What’s the square root of 1
1
What do you have to remember when labelling the unit circle
The angle is ALWAYS from the x axis so don’t mix up 30 degrees with 60 degrees in some quadrants
