Apply trigonometry to solve triangles using Law of Sines and Law of Cosines, analyze periodic functions, model wave phenomena, and solve real-world problems in physics and engineering.
Solve for the missing side using Law of Cosines!
Triangle: a = 5, b = 7, C = 60°
Analyze the periodic function!
Function: y = 2sin(2πx/4 + 0)
For any triangle with sides a, b, c and opposite angles A, B, C:
a/sinA = b/sinB = c/sinC
Use when you know: two angles and one side (AAS or ASA), or two sides and a non-included angle (SSA - ambiguous case).
Problem: Triangle: A=30°, B=45°, a=10. Find side b.
Step 1: Using Law of Sines: a/sinA = b/sinB
Step 2: 10/sin30° = b/sin45°
Step 3: 10/(1/2) = b/(√2/2), so 20 = b/(√2/2)
Answer: b = 20(√2/2) = 10√2
Problem: Triangle: a=8, b=6, A=45°. Find angle B.
Step 1: 8/sin45° = 6/sinB
Step 2: sinB = 6sin45°/8 = 6(√2/2)/8 = 3√2/8
Step 3: B = arcsin(3√2/8) ≈ 32.7°
Answer: B ≈ 32.7°