All Six Trigonometric Functions Finding All Six Trigonometric Functions of The Quadrantals

Let us now decrease the value of y and keep the x-value equal to 1 Let is consider an angle in the First Quadrant whose terminal side passes through a point (1, y) Let us now decrease the value of y and keep the x-value equal to 1

Let is consider an angle in the First Quadrant whose terminal side passes through a point (1, y) Let us now decrease the value of y again and keep the x-value equal to 1

Let is consider an angle in the First Quadrant whose terminal side passes through a point (1, y) Let us now decrease the value of y again and keep the x-value equal to 1

Let is consider an angle in the First Quadrant whose terminal side passes through a point (1, y) Let us now decrease the value of y again and keep the x-value equal to 1

The Terminal side passes through the point (1, 0) And When Getting closer and closer to ?

Using a Calculator we could complete the table below The Terminal side passes through the point (1, 0) And When Using a Calculator we could complete the table below

We see the Cosine is getting closer and closer to 1 And the Sine is getting closer and closer to 0

Now we can use these observations to find all Six Trig Functions

What about the Tangent? Remember

Reciprocals

Therefore the Reciprocal is Reciprocals Therefore the Reciprocal is

All Six Trigonometric Functions of

If we made an ordered pair (cosine, sine) It would be (1,0) which were the coordinates of the point that the terminal side passes through when

180

Let us now decrease the value of y and keep the x-value equal to –1 Let is consider an angle in the Second Quadrant whose terminal side passes through a point (–1, y) Let us now decrease the value of y and keep the x-value equal to –1

Let us now decrease the value of y again and keep the x-value equal to –1

The Terminal side passes through the point (–1, 0) And When Getting closer and closer to ?

Using a Calculator we could complete the table below The Terminal side passes through the point (–1, 0) And When Using a Calculator we could complete the table below

We see the Cosine is getting closer and closer to –1 And the Sine is getting closer and closer to 0

Now we can use these observations to find all Six Trig Functions

What about the Tangent? Remember

Reciprocals

All Six Trigonometric Functions of

If we made an ordered pair (cosine, sine) It would be (–1,0) which were the coordinates of the point that the terminal side passes through when

90

Let us now decrease the value of x and keep the y-value equal to 1 Let is consider an angle in the First Quadrant whose terminal side passes through a point (x, 1) Let us now decrease the value of x and keep the y-value equal to 1

Let is consider an angle in the First Quadrant whose terminal side passes through a point (x, 1) Let us now decrease the value of x again and keep the y-value equal to 1

Let is consider an angle in the First Quadrant whose terminal side passes through a point (x, 1) Let us now decrease the value of x again and keep the y-value equal to 1

The Terminal side passes through the point (0, 1) And When Getting closer and closer to ?

Using a Calculator we could complete the table below The Terminal side passes through the point (0, 1) And When Using a Calculator we could complete the table below

We see the Cosine is getting closer and closer to 0 And the Sine is getting closer and closer to 1

Now we can use these observations to find all Six Trig Functions

What about the Tangent? Remember

Reciprocals

All Six Trigonometric Functions of

If we made an ordered pair (cosine, sine) It would be (0,1) which were the coordinates of the point that the terminal side passes through when

270

Let us now decrease the value of x and keep the y-value equal to –1 Let is consider an angle in the Fourth Quadrant whose terminal side passes through a point (x, –1) Let us now decrease the value of x and keep the y-value equal to –1

Let is consider an angle in the Fourth Quadrant whose terminal side passes through a point (x, –1) Let us now decrease the value of x again and keep the y-value equal to –1

The Terminal side passes through the point (0,–1) And When Getting closer and closer to ?

Using a Calculator we could complete the table below The Terminal side passes through the point (0,–1) And When Using a Calculator we could complete the table below

We see the Cosine is getting closer and closer to 0 And the Sine is getting closer and closer to –1

Now we can use these observations to find all Six Trig Functions

What about the Tangent? Remember

Reciprocals

All Six Trigonometric Functions of

If we made an ordered pair (cosine, sine) It would be (0,–1 ) which were the coordinates of the point that the terminal side passes through when

The Coterminal Angle Definition What About 360 Remember The Coterminal Angle Definition

Definition If is the degree measure of an angle, then all angles coterminal with this angle have degree measure where k is an integer.

What About Same As

Summary Summary

If we made an ordered pair (cosine, sine) It would be (1,0) which were the coordinates of the point that the terminal side passes through when

If we made an ordered pair (cosine, sine) It would be (–1,0) which were the coordinates of the point that the terminal side passes through when

If we made an ordered pair (cosine, sine) It would be (0,1) which were the coordinates of the point that the terminal side passes through when

If we made an ordered pair (cosine, sine) It would be (0,–1 ) which were the coordinates of the point that the terminal side passes through when