1 | ||
Wyznacz zbiór wartości funkcji f(x)= | sin2x+cos2x | |
2 |
1 + cos2x | ||
cos2x = | ||
2 |
1 | 1 | |||
f(x) = | (sin2x + cos2x) + | |||
2 | 2 |
√2 − 1 | √2 + 1 | |||
f(R) = [ − | ; | ] | ||
2 | 2 |
2cos2x − 1 | 1 | 1 | 1 | |||||
cos2x = | + | = | cos(2x) + | |||||
2 | 2 | 2 | 2 |
1 | 1 | |||
f(x) = | (sin(2x) + cos(2x) + 1) = | ( √2sin(2x + π/4) + 1) | ||
2 | 2 |