Exploring Trigonometry: Sine, Cosine, and Tangent Basics

1. x r y r y x = = = Y Y Y Y Y (x,y) r y Soh Cah Toa q x X X X X X  Trigonometry sinq cosq tanq 0 < q < 90 90 < q < 180 180 < q < 270 270 < q < 360 All + sin+ cos + tan+ sinq> 0 cos q > 0 tanq > 0 + + + sinq> 0 cosq < 0 tanq < 0 + sinq< 0 cosq < 0 tanq > 0 sinq< 0 cosq > 0 tanq < 0 + + All sin tan cos

2. Y Y X X 1 √ 2 sin45˚ = √2 S A 1 1 √ 2 cos45˚ = 45˚ T C 1 1 1 tan45˚ = √ 3 2 1 2 sin60˚ = sin30˚ = 30˚ 2 √3 1 2 √ 3 2 cos60˚ = cos30˚ = 60˚ √ 3 1 1 √ 3 tan60˚ = tan30˚ = 1 CAST diagram 180 - q key angle q q q q q 180 + q 360 - q

3. sinA a sinB b sinC c a sinA b sinB c sinC = = = = b2 + c2 - a2 2 b c cosA = c Pythagoras’ theorem c2 = a2 + b2 a q b Right angled triangle sinq= a/c Soh Cah Toa cosq= b/c tanq= a/b The Sine Rule B c a A C b The Cosine Rule a2 = b2 + c2 - 2 b c cosA b2 = a2 + c2 - 2 a c cosB c2 = a2 + b2 - 2 a b cosC