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
