Finding sin(75°) Exactly

Trigonometry · Axiom Academy

EXAMPLE Finding sin(75°) Exactly Using the angle addition formula to find exact trigonometric values Excellent work! You've successfully found sin(75°) exactly using the angle addition formula. Here's what we learned: Angle Decomposition: When we need exact values for non-standard angles, we can break them into sums or differences of special angles (30°, 45°, 60°) Sum Formula Application: sin(A + B) = sin(A)cos(B) + cos(A)sin(B) is our key tool for finding exact values Special Angle Values: Memorizing exact values for 30°, 45°, and 60° allows us to find exact values for many other angles Radical Simplification: The final answer (√6 + √2)/4 cannot be simplified further - leave radicals in exact form rather than using decimals Alternative Decompositions: We could also use 75° = 120° - 45° or 75° = 30° + 45° (same result, different approach) This technique extends to finding exact values for cos(75°), tan(15°), sin(105°), and many other angles. The key is recognizing which special angles to combine!

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