Question

利用和(差)角公式求下列各三角函数的值①sin(-7π/12) ②cos(-61π/12) ③tan35

利用和(差)角公式求下列各三角函数的值①sin(-7π/12) ②cos(-61π/12) ③tan35π/12

Answer 1

sin(-7π/12) = sin(-π/3-π/4)
= sin(-π/3)cos(-π/4) + cos(-π/3)sin(-π/4)
= -√3/2*√2/2 + 1/2 * (-√2/2)
= -(√6+√2) / 4

cos(-61π/12) = cos(61π/12) = cos(5π+π/12）
= -cos(π/12) = -cos(π/3-π/4）
= -cos(π/3)cos(π/4)-sin(π/3)sin(π/4)
= -1/2*√2/2 - √3/2*√2/2
= -(√2+√6)/4

tan(35π/12) = tan(3π-π/12) = tan(-π/12) = tan(π/4-π/3)
= (tanπ/4-tanπ/3) / (1+tanπ/4tanπ/3)
= (1-√3)/(1+√3)
= (1-√3)² /(1-3)
= (4-2√3)/(-2)
= √3-2