In this lesson:
After this lesson, you will be able to:
SOH-CAH-TOA gives us three ratios:
But there are six trig functions total. What are the other three?
Each trig function has a reciprocal partner:
Pairs with the function that does NOT share its first letter:
The letters deliberately cross over.
The reciprocal ratios use the same sides, just flipped.
Answer these without looking back:
Think about it before advancing...
To find a reciprocal trig value:
Step 1: Find the base trig value (sin, cos, or tan)
Step 2: Flip it — take the reciprocal
Step 3: Rationalize the denominator if needed
The angle stays the same. You flip the output, not the input.
Step 1: Find the base value
Step 2: Flip it
No rationalization needed — the answer is 2.
Step 2: Flip and rationalize
Method 1: Flip tangent
Method 2: Use
What is ?
Flip it, then rationalize if needed...
Note: csc and sec are undefined where sin or cos = 0.
A function times its reciprocal always equals 1:
This is the key identity for ACT simplification.
Simplify:
Step 1: Recognize reciprocal pairs
Step 2: Add the results
Strategy: Convert to sin and cos first
The cancels, leaving just .
A. B. C. D. E.
Solve it, then advance...
Answer: , so → C
Identify the reciprocal pairs...
Answer: → B
Remember:
Watch out:
Up next: Trigonometric identities and equations
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Reciprocal trig functions (csc, sec, cot)