已知三角形ABC的内角A,B,C所对的边分别为a,b,c,且a=2,B=5/3 (1)若b=4,求sinA的值还有一道题目.已知函数f(x)=ax(x是幂)-1/ax(x是幂)+1 且a>1(1)判断函数f(x)的奇偶性(2)求f(x)的值域
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![已知三角形ABC的内角A,B,C所对的边分别为a,b,c,且a=2,B=5/3 (1)若b=4,求sinA的值还有一道题目.已知函数f(x)=ax(x是幂)-1/ax(x是幂)+1 且a>1(1)判断函数f(x)的奇偶性(2)求f(x)的值域](/uploads/image/z/8616037-13-7.jpg?t=%E5%B7%B2%E7%9F%A5%E4%B8%89%E8%A7%92%E5%BD%A2ABC%E7%9A%84%E5%86%85%E8%A7%92A%2CB%2CC%E6%89%80%E5%AF%B9%E7%9A%84%E8%BE%B9%E5%88%86%E5%88%AB%E4%B8%BAa%2Cb%2Cc%2C%E4%B8%94a%3D2%2CB%3D5%2F3+%281%29%E8%8B%A5b%3D4%2C%E6%B1%82sinA%E7%9A%84%E5%80%BC%E8%BF%98%E6%9C%89%E4%B8%80%E9%81%93%E9%A2%98%E7%9B%AE.%E5%B7%B2%E7%9F%A5%E5%87%BD%E6%95%B0f%28x%29%3Dax%28x%E6%98%AF%E5%B9%82%29-1%2Fax%28x%E6%98%AF%E5%B9%82%29%2B1+%E4%B8%94a%3E1%281%29%E5%88%A4%E6%96%AD%E5%87%BD%E6%95%B0f%28x%29%E7%9A%84%E5%A5%87%E5%81%B6%E6%80%A7%282%29%E6%B1%82f%28x%29%E7%9A%84%E5%80%BC%E5%9F%9F)
已知三角形ABC的内角A,B,C所对的边分别为a,b,c,且a=2,B=5/3 (1)若b=4,求sinA的值还有一道题目.已知函数f(x)=ax(x是幂)-1/ax(x是幂)+1 且a>1(1)判断函数f(x)的奇偶性(2)求f(x)的值域
已知三角形ABC的内角A,B,C所对的边分别为a,b,c,且a=2,B=5/3 (1)若b=4,求sinA的值
还有一道题目.
已知函数f(x)=ax(x是幂)-1/ax(x是幂)+1 且a>1
(1)判断函数f(x)的奇偶性
(2)求f(x)的值域
已知三角形ABC的内角A,B,C所对的边分别为a,b,c,且a=2,B=5/3 (1)若b=4,求sinA的值还有一道题目.已知函数f(x)=ax(x是幂)-1/ax(x是幂)+1 且a>1(1)判断函数f(x)的奇偶性(2)求f(x)的值域
(1)
因为 cosB = 3/5
所以 sinB = 4/5
根据正弦定理
a/sinA = b/sinB
所以 2/sinA = 4/(4/5)
所以 sinA = 2/5
(2)
S△ABC = acsinB/2 = 4
所以 2c×(4/5)/2 = 4
c = 5
根据余弦定理
b² = a² + c² - 2ac CosB
= 4 + 25 - 2×2×5×(3/5)
= 17
所以 b = √17
f(-x)
= [a^(-x) - 1]/[a^(-x) + 1 ]
= (1 - a^x)/(1 + a^x)
= -f(x)
所以 f(x)是奇函数
f(x)
= (a^x - 1)/(a^x + 1)
= (a^x + 1 - 2)/(a^x + 1)
= 1 - 2/(a^x + 1)
因为 a > 1
所以 a^x > 0
所以 a^x + 1 > 1
所以 0 < 2/(a^x + 1) < 2
所以 -2 < -2/(a^x + 1) < 0
所以 -1 < 1 -2/(a^x + 1) < 1
所以值域是 (-1 ,1)