Section 4.4 Trigonometric Functions of Any Angle

Blogpost 3rd Hour Pre Calc.

Today we learned about Reference Angles and Inverse Trigonometric Functions

REFERENCE ANGLES

• The values of the trigonometric functions of angles greater than 90° (or less than 0° ) can be determined from their values at corresponding acute angles called REFERENCE ANGLES.

• Definition: Letθ be an angle in standard position. Its REFERENCE ANGLE is the acute angleθ'formed by the TERMINAL SIDE ofθ and the HORIZONTAL AXIS.

• In short terms, Reference Angles are always Acute and every angle has one. The reference angle is the angle formed between the horizontal X-axis and the terminal side of the angle that intersects the origin.

In order to find reference

angles you need to determine which quadrant you want the reference angle to be in.

Different Reference Angles exist in all of the 4 quadrants. The

way to find out the reference angle in the designated quadrant is in the following

formulas.

In quadrant 1

:

1=

In quadrant 2:

1=-

In quadrant 3:

1=-

In quadrant 4:

1=2-

Today we also learned about identity inverses:

For example......

If you were assigned to find the angle measure algebraically when given the equation sin

= 1 you wouldn't be able to find solve and find the correct angle measure.

Today we learned that by taking the sine or cosine inverse of whatever the equation equals, we can find the 2 separate corresponding angle measures.

For example sin

= 1

In order to determine

you would plug in sin-1(1) and it would give you 90 degrees or /2 radians.

Almost always, with the exception of 1,-1, and 0, there is a corresponding value in the circle where the sin-1 value is the same. One example is when sin = 1/2, there will be two angle measures; one in the first quadrant and one in the second quadrant where both sin values are positive.