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受欢迎的三角函数 >

arccos(cos((15pi)/4))

解答

arccos (cos (\frac{15 π}{4}))

解答

\frac{π}{4}

+1

十进制

45

求解步骤

arccos (cos (\frac{15 π}{4}))

Use the inverse trig property:

\frac{π}{4}

arccos (cos (\frac{15 π}{4}))

对于

0 \leq x \leq π, a rccos (cos (x)) = x

使用三角恒等式改写:

cos (\frac{15 π}{4}) = cos (\frac{7 π}{4})

cos (\frac{15 π}{4})

cos (x + 2 π \cdot k) = cos (x)

= cos (\frac{15 π}{4} - 1 \cdot 2 π)

= cos (\frac{7 π}{4})

= arccos (cos (\frac{7 π}{4}))

使用三角恒等式改写:

cos (\frac{15 π}{4}) = cos (\frac{π}{4})

cos (\frac{15 π}{4})

cos (x) = cos (2 π - (x))

= cos (2 π - \frac{7 π}{4})

= cos (\frac{π}{4})

= arccos (cos (\frac{π}{4}))

0 \leq \frac{π}{4} \leq π

= \frac{π}{4}

= \frac{π}{4}

流行的例子

sin(arctan(4/3))

sin (arctan (\frac{4}{3}))

cos (0.6)

arctan (\frac{8}{15})

sec (1 5^{\circ})

sin (\frac{1}{4})