Directed (ASTC) or Reference Trigonometric Angles

Trigonometry allows for angles of over 180⁰ called Directed or Reference Angles

Sin A = O/ H Cos A = A/H Tan A = O/A

Csc A = 1/Sin Sec A = 1/Cos Cot A = 1/Tan

Csc A = H/O Sec A = H/A Cot A = A/O

Sin = +/+ All Angles = +/+

+ +

+ +

+ +

- -

+ +

Tan = +/+ Cos = +/+

	I	II	III	IV
Sin	+/+	+/+	-/+	-/+	1/Sin	Csc
Cos	+/+	-/+	-/+	+/+	1/Cos	Sec
Tan	+/+	-/+	+/+	-/+	1/Tan	Cot

####################################################################

Special Trigonometric Angles or Values of: 0⁰ 90⁰ 180⁰ 270⁰ 360⁰+

The Triangles representing these Special Angles “do not exist”.

All small sides of these Triangles = 0 while the hypotenuse and other side = 4.

Therefore since this is an impossibility then the Traingles do not actually exist.

But, they do allow a visual representation for values of these Special Angles.

90⁰

4

4 0⁰

180⁰ 4

4

270⁰

0/4 = 0 4/4 = 1 4/0 = ¥

	I	II	III	IV
Sin	0	1	0	1	1/Sin
Cos	1	0	1	0	1/Cos
Tan	0	¥	0	¥	1/Tan

####################################################################

Directed Angles - Co-Terminal Angles - General Angles

Directed Angles are CW = + or CCW = -

Co-Terminal Angles have a Sum of 360⁰

General Angles are greater than 360⁰

+130⁰ +60⁰

-230⁰ -300⁰

+210⁰ +320⁰

-40⁰

-150⁰

####################################################################