arctan(cot((3pi)/4))

解答

arctan (cot (\frac{3 π}{4}))

- \frac{π}{4}

十进制

- 45

求解步骤

arctan (cot (\frac{3 π}{4}))

使用三角恒等式改写:

cot (\frac{3 π}{4}) = tan (- \frac{π}{4})

cot (\frac{3 π}{4})

tan (\frac{π}{2} - x) = cot (x)

= tan (\frac{π}{2} - \frac{3 π}{4})

= tan (- \frac{π}{4})

= arctan (tan (- \frac{π}{4}))

Use the inverse trig property:

- \frac{π}{4}

arctan (tan (- \frac{π}{4}))

对于

- \frac{π}{2} < x < \frac{π}{2}, a rc t an (t an (x)) = x

- \frac{π}{2} < - \frac{π}{4} < \frac{π}{2}

= - \frac{π}{4}

= - \frac{π}{4}

- \frac{cos ^{3} ( π )}{3}

cos (arctan (- \frac{10}{3}))

sin (35. 5^{\circ})

cos (5 0^{\circ}) + sin (5 0^{\circ})

cos^{2} (3) + sin^{2} (3)