Sum and Difference Sine Formulas (Finding Exact
www.iTutoring.com -‐ NOTES
Sum and Difference Sine Formulas (Finding Exact Values)
Name _________________________________ Date ___________________ Period _______
The Sine of two angles being added together... sin (! + ") = sin ! cos " + cos ! sin "
The Sine of the difference of two angles... sin (! – ") = sin ! cos " – cos ! sin "
Sum sin (! + ") = sin ! cos " + cos ! sin "
Difference sin (! – ") = sin ! cos " – cos ! sin "
Find the exact value of the following expressions: express 75° using common angles 0° 30° 45° 60° 90° 120° 135° 150° 180° sin 75°
Sum sin (! + ") = sin ! cos " + cos ! sin "
Difference sin (! – ") = sin ! cos " – cos ! sin "
Find the exact value of the following expressions: express 15° using common angles 0° 30° 45° 60° 90° 120° 135° 150° 180° sin 15°
Sum sin (! + ") = sin ! cos " + cos ! sin "
Difference sin (! – ") = sin ! cos " – cos ! sin "
Find the exact value of the following expressions: express
7π using common angles 12 0π 2π 3π 4π 6π 8π 12 12 12 12 12 12
9π 12
10π 12π 12 12
sin 7π 12
© iTutoring.com Sum and Difference Sine Formulas (Finding Exact Values) Pg. 2
Sum sin (! + ") = sin ! cos " + cos ! sin "
Difference sin (! – ") = sin ! cos " – cos ! sin "
Find the exact value of the following expressions: express
π using common angles 12 0π 2π 3π 4π 6π 8π 12 12 12 12 12 12
9π 12
10π 12π 12 12
sin π
12
Sum sin (! + ") = sin ! cos " + cos ! sin "
Difference sin (! – ") = sin ! cos " – cos ! sin "
Find the exact value of the following expressions: express 165° using common angles 0° 30° 45° 60° 90° 120° 135° 150° 180° sin 165°
© iTutoring.com Sum and Difference Sine Formulas (Finding Exact Values) Pg. 3
Sum sin (! + ") = sin ! cos " + cos ! sin "
Difference sin (! – ") = sin ! cos " – cos ! sin "
Find the exact value of the following expressions: express
5π using common angles 12 0π 2π 3π 4π 6π 8π 12 12 12 12 12 12
9π 12
10π 12π 12 12
sin 5π 12
Sum sin (! + ") = sin ! cos " + cos ! sin "
Difference sin (! – ") = sin ! cos " – cos ! sin "
Find the exact value of the following expressions: sin 10° cos 20° + cos 10° sin 20°
sin 105° cos 45° – cos 105° sin 45°
© iTutoring.com Sum and Difference Sine Formulas (Finding Exact Values) Pg. 4
Sum sin (! + ") = sin ! cos " + cos ! sin "
Difference sin (! – ") = sin ! cos " – cos ! sin "
Find the exact value of the following expressions: sin
7π 7π π π cos – cos sin 12 12 12 12
sin
5π 5π π π cos + cos sin 18 18 18 18
Sum sin (! + ") = sin ! cos " + cos ! sin "
Difference sin (! – ") = sin ! cos " – cos ! sin "
© iTutoring.com Sum and Difference Sine Formulas (Finding Exact Values) Pg. 5
Sum and Difference Sine Formulas (Finding Exact Values)
Name _________________________________ Date ___________________ Period _______
The Sine of two angles being added together... sin (! + ") = sin ! cos " + cos ! sin "
The Sine of the difference of two angles... sin (! – ") = sin ! cos " – cos ! sin "
Sum sin (! + ") = sin ! cos " + cos ! sin "
Difference sin (! – ") = sin ! cos " – cos ! sin "
Find the exact value of the following expressions: express 75° using common angles 0° 30° 45° 60° 90° 120° 135° 150° 180° sin 75°
Sum sin (! + ") = sin ! cos " + cos ! sin "
Difference sin (! – ") = sin ! cos " – cos ! sin "
Find the exact value of the following expressions: express 15° using common angles 0° 30° 45° 60° 90° 120° 135° 150° 180° sin 15°
Sum sin (! + ") = sin ! cos " + cos ! sin "
Difference sin (! – ") = sin ! cos " – cos ! sin "
Find the exact value of the following expressions: express
7π using common angles 12 0π 2π 3π 4π 6π 8π 12 12 12 12 12 12
9π 12
10π 12π 12 12
sin 7π 12
© iTutoring.com Sum and Difference Sine Formulas (Finding Exact Values) Pg. 2
Sum sin (! + ") = sin ! cos " + cos ! sin "
Difference sin (! – ") = sin ! cos " – cos ! sin "
Find the exact value of the following expressions: express
π using common angles 12 0π 2π 3π 4π 6π 8π 12 12 12 12 12 12
9π 12
10π 12π 12 12
sin π
12
Sum sin (! + ") = sin ! cos " + cos ! sin "
Difference sin (! – ") = sin ! cos " – cos ! sin "
Find the exact value of the following expressions: express 165° using common angles 0° 30° 45° 60° 90° 120° 135° 150° 180° sin 165°
© iTutoring.com Sum and Difference Sine Formulas (Finding Exact Values) Pg. 3
Sum sin (! + ") = sin ! cos " + cos ! sin "
Difference sin (! – ") = sin ! cos " – cos ! sin "
Find the exact value of the following expressions: express
5π using common angles 12 0π 2π 3π 4π 6π 8π 12 12 12 12 12 12
9π 12
10π 12π 12 12
sin 5π 12
Sum sin (! + ") = sin ! cos " + cos ! sin "
Difference sin (! – ") = sin ! cos " – cos ! sin "
Find the exact value of the following expressions: sin 10° cos 20° + cos 10° sin 20°
sin 105° cos 45° – cos 105° sin 45°
© iTutoring.com Sum and Difference Sine Formulas (Finding Exact Values) Pg. 4
Sum sin (! + ") = sin ! cos " + cos ! sin "
Difference sin (! – ") = sin ! cos " – cos ! sin "
Find the exact value of the following expressions: sin
7π 7π π π cos – cos sin 12 12 12 12
sin
5π 5π π π cos + cos sin 18 18 18 18
Sum sin (! + ") = sin ! cos " + cos ! sin "
Difference sin (! – ") = sin ! cos " – cos ! sin "
© iTutoring.com Sum and Difference Sine Formulas (Finding Exact Values) Pg. 5
