Circular Trigonometry Question

Question

Find an exact value by using an appropriate addition or subtraction formula.

Find the exact value for sin(-195)°

Answer 1

sin(-195°) can be calculated in two steps showing the result as a function of the first quadrant angle and then using formula for sine of difference of angles.

sin(-195°) = sin(360°-195°) = sin(165°) = sin(180°-15°) = sin(15°)

sin(15°) = sin(45°-30°) = sin(45°)cos(30°)-cos(45°)sin(30°) = √2/2*√3/2-√2/2*1/2 = (√6-√2)/4

Answer 2

sin-195 = 0.259

sin-195 = sin165 = sin 15

sin2x = 2sinxcosx

sin30 = 2sin15cos15

sin15 = sin30/2cos15

sin30 = 1/2

cos15 = + or - sqr(1+cos30/2) = + or - sqr(.933) = 0.966

sin15=(1/2)/2(.966) = .1/4(.966) = 0.259 rounded to 3 decimal places