Trigonometry (Identities and Addition Formulae)

Question 1

What is

tan θ

Answer 1

sin θ/ cos θ

Question 2

What is

csc θ

Answer 2

1 / sin θ

s for one, c for the inverse

Question 3

What is

sec θ

Answer 3

1 / cos θ

c for one, s for the inverse

Question 4

What is

cot θ

Answer 4

cos θ / sin θ or 1 / tan θ

Question 5

(sin θ)^2 + (cos θ)^2 = ?

This is a Pythagorean identity

Answer 5

1

Question 6

(tan θ)^2 + 1 = ?

This is a Pythagorean identity

Answer 6

(sec θ)^2

Question 7

(cot θ)^2 + 1 = ?

This is a Pythagorean identity

Answer 7

(csc θ)^2

Question 8

What is an even function?

Answer 8

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)

Question 9

What is an odd function?

Answer 9

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)

Question 10

About what line or axis are even functions symmetrical?

Answer 10

The y-axis

Question 11

About what line or axis are odd functions symmetrical?

Answer 11

The line y = x

Question 12

Which is trig function is odd or even?

1. Sine function
2. Cosine function
3. Tangent function

Answer 12

1. Odd
2. Even
3. Odd

Question 13

What is

Sin (A + B)

where A and B are two angles

Answer 13

Sin(A)Cos(B) + Sin(B)Cos(A)

Question 14

What is

Cos (A + B)

where A and B are two angles

Answer 14

Cos(A)Cos(B) - Sin(A)Sin(B)

Question 15

What is

Tan (A + B)

Where A and B are two angles and Tan x = Sin x / Cos x

Answer 15

Tan (A) + Tan (B) / 1 - Tan(A)Tan(B)

note the subtle differences

Question 16

What is

Sin (A - B)

where A and B are two angles

Answer 16

Sin(A)Cos(-B) + Sin(-B)Cos(A)

Sin(A)Cos(B) - Sin(B)Cos(A)

Question 17

What is

Cos (A - B)

where A and B are two angles

Answer 17

Cos(A)Cos(B) - Sin(A)Sin(-B)

Cos(A)Cos(B) + Sin(A)Sin(B)

Question 18

What is

Tan (A - B)

where A and B are two angles

Answer 18

Tan (A) - Tan (B) / 1 + Tan(A)Tan(B)

note the subtle differences

Question 19

When A=B, what is

Sin (A + B)?

Answer 19

Sin (2A) = 2Sin(A)Cos(A)

Question 20

When A=B, what is

Cos (A + B)?

Answer 20

Cos (2A) = (Cos(A))^2 - (Sin(A))^2

Question 21

When A=B, what is

Tan (A + B)?

Answer 21

Tan (2A) = 2Tan(A) / 1 -(Tan(A))^2

Question 22

How else can we rewrite

Cos (3A)

in order to use the addition formula?

Answer 22

Cos (2A) + Cos (A)

Then you let your first angle be ‘2A’ and your second be ‘A’

Question 23

What is

Cos (x ± 2π)

Answer 23

Cos (x)

The cosine function repeats itself every 2π rads or 360 degrees

Question 24

What is

Sin (x ± 2π)

Answer 24

Sin (x)

The sine function repeats itself every 2π rads or 360 degrees

Question 25

What is

Sec (x ± 2π)

Answer 25

Sec (x)

Like the cosine function, the secant function repeats itself every 2π rads or 360 degrees

Question 26

What is

Csc (x ± 2π)

Answer 26

Csc (x)

Like the sine function, the cosecant function repeats itself every 2π rads or 360 degrees

Question 27

What is

Tan (x ± π)

Answer 27

Tan (x)

The tangent function repeats itself every π rads or 180 degrees

Question 28

What is

Cot (x ± π)

Answer 28

Cot (x)

Like the tangent function, the cotangent function repeats itself every π rads or 180 degrees