Equivalent Ratio Problem Solving Procedure

Co-Function vs Supplementary equations

Check if you are going to use Co-Function Identities or Supplementary Function Identities If the function equals the function, then its Supplementary Function Identities If the function equals its ‘enemy’ then its Co-Function Identities

Prove Expression (Co-Function)

Given: 2 angles, 2 trig functions Required: Proof statements

They want you to prove two trig ratios are the same. We will use this equation, they are enemies.

Step 1. Draw the angles out

You have both angles. Draw their general direction.

Step 2. Determine whether to Add or Subtract

There are 2 cases that can happen when you draw them.

Case A - Angles same Quadrant

Both angles are in the same quadrant and they both add up to $90^o$ In this case, you would use general Co-Function Identities So, $\frac{\pi }{2}-{\theta }_1={\theta }_2$

Case B - Angles different quadrants

Angles are in seperate quadrants. but there is a $90^o$ disparity between them. The disparity is $90^o$ So you know the other one if you add/subtract $\frac{\pi }{2}$

Step 3 Prove

Alternate Example with CASE B

Find Angle (Co-Function)

Given: 1 angle, 2 trig functions, quadrant of other angle Required: Other angle

Step 1. Draw known angle

Step 2. Determine case A or B

angle ? lies in the same quadrant as our other angle. This is case A Thus, we know both angles add up to 90

Step 3. Prove

Alternate Example with CASE B