Warm Up Identify the Vertical Shift, Amplitude, Maximum and Minimum, Period, and Phase Shift of each function Y = 3 + 6cos(8x) Y = 2 - 4sin( x + 3) Y = 3cos(x - ) -2

Addition and subtraction of sine, cosine and tangent We will be able to use the addition and subtraction formulas of sine, cosine, and tangent to determine exact trigonometric values

EXAMPLES Example 1 Calculate sin(75°) by applying the addition formula: sin(75°) = sin(30°)*cos(45°) + cos(30°)*sin(45°) =

Calculate cos(75°) by applying the addition formula: EXAMPLE 2 Calculate cos(75°) by applying the addition formula: Note that 75° = 30° + 45°. cos(75°) = cos(30°)*cos(45°) - sin(30°)*sin(45°) = ???

Answer to Example 2

Explore What is the solution to sin(30) + sin(60)? Is it the same as the solution of sin(90)? What about cos(55) – cos(10) And cos(45)

+/- of Sine In order to solve addition and subtraction of sine function, we have to set them up correctly Sin(x + y) = sin(x)cos(y) + cos(x)sin(y) Sin(x - y) = sin(x)cos(y) - cos(x)sin(y)

Addition Example What is the solution of sin(90)? Lets try and break it down into 30° and 60°

Subtraction Example Lets evaluate sin(15°) Now lets break it down into 45° and 30° and check:

Practice on your own What is sin(135°)? What if we break it down into 100° and 35°? What if we make it 140° and 5°

+/- of Cosine Cosine follows similar but different rules cos(x + y) = cos(x)cos(y) - sin(x)sin(y) cos(x - y) = cos(x)cos(y) + sin(x)sin(y)

Addition example Cos(60°) = What if we break it down into 30° and 30°?

Subtraction example What is cos(90°) Break it down into 100° and 10°

Your turn Cos of 120°? Break it down into 100° and 20° Now try it as 150° and 30°

Last one……TAN

Example Tan(50) = What if we break it down into 25° and 25°

Your turn Tan(300) = What if we break it down into 360° and 60°?

Cumulative practice Find the sin(210°) using 100 ° and 110° Find the cos(210°) using 350° and 140° Find the tan(210°) using 150° and 60°