Math Analysis Notes
Notes 6.5 Double and Half-angle Formulas
Double Angle Formulas:
Use the angle sum formulas to develop new formulas for double angles.
Circle the new formulas!
[pic]
[pic]
[pic]
Ex 1] Find the EXACT values of [pic], using the double-angle formulas, given:
[pic].
[pic]
Example 2.] Verify the identity algebraically.
[pic]
Half-Angle Formulas:
sin [pic] = [pic] cos [pic] = [pic] tan [pic] = [pic] = [pic]
** The signs of sin [pic] and cos [pic] depend on the quadrant in which [pic] lies.
Example 3.] Use the half-angle formulas to find sin15(
Example 4.] Given that tan u = [pic], [pic] < u < 2[pic], use the half-angle formulas to find the EXACT values of: cos [pic] and tan [pic].
HW: pp. 455 – 457 #7, 11, 17, 19, 21, 25, 30 (hint: use angle sum formulas, 3x = 2x +1x), 35, 41
Worksheet to review 6.4 material – quiz 6.4 next class!
Warm-up
Use sum or difference formulas to find the exact value of:
1. cos 165°
2. Given: [pic]. Find [pic].
In which quadrant would the following angles lie?
3. [pic] 4. [pic] 5. [pic]
6. 15[pic] is half of what? 7. [pic] is half of what?
8. If [pic] then [pic]
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MEMORIZE
THESE!!
MEMORIZE
THESE!!
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