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受欢迎的三角函数 >

sin(arcsin(2/3)+arccos(1/2))

解答

sin (arcsin (\frac{2}{3}) + arccos (\frac{1}{2}))

解答

\frac{1}{3} + \frac{15}{6}

+1

十进制

0.97883 \dots

求解步骤

sin (arcsin (\frac{2}{3}) + arccos (\frac{1}{2}))

使用三角恒等式改写:

sin (arcsin (\frac{2}{3})) cos (arccos (\frac{1}{2})) + cos (arcsin (\frac{2}{3})) sin (arccos (\frac{1}{2}))

sin (arcsin (\frac{2}{3}) + arccos (\frac{1}{2}))

使用角和恒等式:

sin (s + t) = sin (s) cos (t) + cos (s) sin (t)

= sin (arcsin (\frac{2}{3})) cos (arccos (\frac{1}{2})) + cos (arcsin (\frac{2}{3})) sin (arccos (\frac{1}{2}))

= sin (arcsin (\frac{2}{3})) cos (arccos (\frac{1}{2})) + cos (arcsin (\frac{2}{3})) sin (arccos (\frac{1}{2}))

使用三角恒等式改写:

sin (arcsin (\frac{2}{3})) = \frac{2}{3}

利用以下特性:

sin (arcsin (x)) = x

= \frac{2}{3}

使用三角恒等式改写:

cos (arccos (\frac{1}{2})) = \frac{1}{2}

利用以下特性:

cos (arccos (x)) = x

= \frac{1}{2}

使用三角恒等式改写:

cos (arcsin (\frac{2}{3})) = \frac{5}{3}

cos (arcsin (\frac{2}{3}))

使用三角恒等式改写:

cos (arcsin (\frac{2}{3})) = 1 - (\frac{2}{3})^{2}

利用以下特性:

cos (arcsin (x)) = 1 - x^{2}

= 1 - (\frac{2}{3})^{2}

= 1 - (\frac{2}{3})^{2}

化简

= \frac{5}{3}

使用三角恒等式改写:

sin (arccos (\frac{1}{2})) = \frac{3}{2}

sin (arccos (\frac{1}{2}))

使用三角恒等式改写:

sin (arccos (\frac{1}{2})) = 1 - (\frac{1}{2})^{2}

利用以下特性:

sin (arccos (x)) = 1 - x^{2}

= 1 - (\frac{1}{2})^{2}

= 1 - (\frac{1}{2})^{2}

化简

= \frac{3}{2}

= \frac{2}{3} \cdot \frac{1}{2} + \frac{5}{3} \cdot \frac{3}{2}

化简

\frac{2}{3} \cdot \frac{1}{2} + \frac{5}{3} \cdot \frac{3}{2} : \frac{1}{3} + \frac{15}{6}

\frac{2}{3} \cdot \frac{1}{2} + \frac{5}{3} \cdot \frac{3}{2}

\frac{2}{3} \cdot \frac{1}{2} = \frac{1}{3}

\frac{2}{3} \cdot \frac{1}{2}

交叉约分:

2

= \frac{1}{3}

\frac{5}{3} \cdot \frac{3}{2} = \frac{15}{6}

\frac{5}{3} \cdot \frac{3}{2}

分式相乘:

\frac{a}{b} \cdot \frac{c}{d} = \frac{a \cdot c}{b \cdot d}

= \frac{5 3}{3 \cdot 2}

数字相乘:

3 \cdot 2 = 6

= \frac{5 3}{6}

化简

53 : 15

53

使用根式运算法则:

a b = a \cdot b

53 = 5 \cdot 3

= 5 \cdot 3

数字相乘:

5 \cdot 3 = 15

= 15

= \frac{15}{6}

= \frac{1}{3} + \frac{15}{6}

= \frac{1}{3} + \frac{15}{6}

流行的例子

cot (7 3^{\circ})

sqrt((183*9.8)/(sin(2*45)))

\frac{183 \cdot 9.8}{sin ( 2 \cdot 45 )}

4(cos((5pi)/6)+isin((5pi)/6))

4 (cos (\frac{5 π}{6}) + i sin (\frac{5 π}{6}))

arctan (- 0.9)

3 cos (\frac{5 π}{3})