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Radians & Degrees

Angles in Standard Position Revisited

Trig. Functions & Graphs

Transformations

Trig. Identities

Trig. Equations

Summary&Test

 

 

UNIT 7 : TRIGONOMETRIC FUNCTIONS

 LESSON 2: ANGLES IN STANDARD POSITION

 

Angles in Standard Position:

 

Definition: An angle is in standard position if it has its vertex at the origin and initial arm along the positive x-axis. The terminal arm is found by rotating

the initial arm about the origin to a terminal position in one of the 4 quadrants. The rotation is positive if it is in the counter clockwise direction and negative

if in the clockwise direction.

 

 

 

 

 

 

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Note that all three ratios are positive for a first quadrant angle.

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Note that sine is positive and cosine and tangent are negative for a second quadrant angle.

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Note that tan is positive and sine and cosine are negative for a third quadrant angle.

 

 

 

 

 

 

Note that cos is positive and sine and tangent are negative for a fourth quadrant angle.

 

 

The CAST rule:

 

The CAST RULE is a memory aid which tells us the sign of the trig ratios in the various quadrants.

In the first quadrant ALL are positive. This is denoted using the letter A.

In the second quadrant, SINE is positive. This is denoted by the letter S.

[ the other two ratios are negative ]

In the third quadrant, TANGENT is positive. This is denoted by the letter T.

[ the other two ratios are negative ]

In the fourth quadrant, COSINE is positive. This is denoted by the letter C.

[ the other two ratios are negative ].

 

 

 

 

 

 

 

Special Triangles:

 

These triangles enable us to find the trig ratios of acute angles 300, 450 , 600 and their related angles

 

 

 

 

 

 

 

 

 


 

 

 

 

 

 

Trig. Ratios of any Angles in Standard Position:

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

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