Trigonometry (Identities and Addition Formulae) Flashcards
What is
tan θ
sin θ/ cos θ
What is
csc θ
1 / sin θ
s for one, c for the inverse
What is
sec θ
1 / cos θ
c for one, s for the inverse
What is
cot θ
cos θ / sin θ or 1 / tan θ
(sin θ)^2 + (cos θ)^2 = ?
This is a Pythagorean identity
1
(tan θ)^2 + 1 = ?
This is a Pythagorean identity
(sec θ)^2
(cot θ)^2 + 1 = ?
This is a Pythagorean identity
(csc θ)^2
What is an even function?
This is a function that has the same output for positive and negative inputs of the same number
For an even function, f(x) = f(-x)
What is an odd function?
This is a function where the output it has for positive input of a number is equal to the output with the negative inputs of the same number multiplied by -1
For an even function, f(-x) = -f(x)
About what line or axis are even functions symmetrical?
The y-axis
About what line or axis are odd functions symmetrical?
The line y = x
Which is trig function is odd or even?
- Sine function
- Cosine function
- Tangent function
- Odd
- Even
- Odd
What is
Sin (A + B)
where A and B are two angles
Sin(A)Cos(B) + Sin(B)Cos(A)
What is
Cos (A + B)
where A and B are two angles
Cos(A)Cos(B) - Sin(A)Sin(B)
What is
Tan (A + B)
Where A and B are two angles and Tan x = Sin x / Cos x
Tan (A) + Tan (B) / 1 - Tan(A)Tan(B)
note the subtle differences
What is
Sin (A - B)
where A and B are two angles
Sin(A)Cos(-B) + Sin(-B)Cos(A)
Sin(A)Cos(B) - Sin(B)Cos(A)
What is
Cos (A - B)
where A and B are two angles
Cos(A)Cos(B) - Sin(A)Sin(-B)
Cos(A)Cos(B) + Sin(A)Sin(B)
What is
Tan (A - B)
where A and B are two angles
Tan (A) - Tan (B) / 1 + Tan(A)Tan(B)
note the subtle differences
When A=B, what is
Sin (A + B)?
Sin (2A) = 2Sin(A)Cos(A)
When A=B, what is
Cos (A + B)?
Cos (2A) = (Cos(A))^2 - (Sin(A))^2
When A=B, what is
Tan (A + B)?
Tan (2A) = 2Tan(A) / 1 -(Tan(A))^2
How else can we rewrite
Cos (3A)
in order to use the addition formula?
Cos (2A) + Cos (A)
Then you let your first angle be ‘2A’ and your second be ‘A’
What is
Cos (x ± 2π)
Cos (x)
The cosine function repeats itself every 2π rads or 360 degrees
What is
Sin (x ± 2π)
Sin (x)
The sine function repeats itself every 2π rads or 360 degrees
What is
Sec (x ± 2π)
Sec (x)
Like the cosine function, the secant function repeats itself every 2π rads or 360 degrees
What is
Csc (x ± 2π)
Csc (x)
Like the sine function, the cosecant function repeats itself every 2π rads or 360 degrees
What is
Tan (x ± π)
Tan (x)
The tangent function repeats itself every π rads or 180 degrees
What is
Cot (x ± π)
Cot (x)
Like the tangent function, the cotangent function repeats itself every π rads or 180 degrees
