9514 1404 393
Answer:
sin: 0, (√(2-√3))/2, 1/2, (√2)/2, (√3)/2, (√(2+√3))/2, 1
cos are the same values in reverse order
Step-by-step explanation:
Given the side ratios of the "special" right triangles, we know that ...
sin(30°) = cos(60°) = 1/2
sin(45°) = cos(45°) = 1/√2 = (√2)/2
sin(60°) = cos(30°) = (√3)/2
Using the half-angle formulas in the second attachment, we can find exact values for the 15° and 75° angles.
sin(15°) = sin(30°/2) = √((1 -cos(30°)/2) = √((1 -(√3)/2)/2) = (√(2 -√3))/2
cos(15°) = √((1 +cos(30°)/2) = √((1 +(√3)/2)/2) = (√(2 +√3))/2
Then the exact table values are ...
- sin(0°) = cos(90°) = 0
- sin(15°) = cos(75°) = (√(2-√3))/2
- sin(30°) = cos(60°) = 1/2
- sin(45°) = cos(45°) = (√2)/2
- sin(60°) = cos(30°) = (√3)/2
- sin(75°) = cos(15°) = (√(2+√3))/2
- sin(90°) = cos(0°) = 1
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Additional comments
The numerical sine and cosine values in the attachment are computed by the spreadsheet functions SIN( ) and COS( ). Those functions require an argument in radians. The RADIANS( ) function converts from degrees to radians.
The "special" right triangles are the isosceles right triangle with side ratios 1:1:√2, and the 30°-60°-90° triangle with side ratios 1:√3:2.
