Odd Even or Negative Angle Identities

Trigonometric Functions - Odd Even or Negative Angle Identities - How it Works - Video

Odd Even or Negative Angle Identities

Odd Even Identities:

Here is the list. It is also called Negative Angle Identities. You can choose how you want to call them.

Odd Even Identities - Sine

Odd Even Identities:

Here we have a look at sine, and why sin(-θ) = -sinθ and why the reciprocal identity is csc(-θ) = -cscθ.

Let's take a look at the points (-π / 2, 1) and (π / 2, 1). If we take the absolute value of each x value, the result is the same. Remember absolute value is a distance so we went π / 2 to the right and to the left. But when we went right, the y-value is 1 and when we go left, the x-value is -1. The only difference is that one number is positive and one is negative. Which is why we can say sin(-θ) = -sinθ.

Using reciprocal identities we can show that the same is true for csc(θ).

Odd Even Identities:

Here we have a look at cosine, and why cos(-θ) = cosθ and why the reciprocal identity is sec(-θ) = secθ.

Let's take a look at the points (-π , 1) and (π , 1). If we take the absolute value of each x value, the result is the same. Remember absolute value is a distance so we went π to the right and to the left. But when we went right, the y-value is -1 and when we go left, the x-value is -1. They have the same v-value. Which is why we can say cos(-θ) = cosθ.

Using reciprocal identities we can show that the same is true for sec(θ).

Odd Even Identities:

Here we have a look at tangent, and why tan(-θ) = -tanθ and why the reciprocal identity is cot(-θ) = -cotθ.

Let's take a look at the points (-4π/3 , -sqrt(3)) and (4π/3 , sqrt(3)). If we take the absolute value of each x value, the result is the same. Remember absolute value is a distance so we went 4π/3 to the right and to the left. But when we went right, the y-value is sqrt(3) and when we go left, the x-value is -sqrt(3). The only difference is that one number is positive and one is negative. Which is why we can say tan(-θ) = -tanθ.

Using reciprocal identities we can show that the same is true for cot(θ).

Example 1

Example 1:

Here we have sin(-π/3).

Now we can use the Odd Even Identity, sin(-θ) = -sinθ.

So sin(-π/3) = - sin(π/3) = - sqrt(3) /2.

Live Worksheet

Teacher - Edpuzzle Link