gaokao 2010 Q4

gaokao · China · shanghai-science Reciprocal Trig & Identities
4. The value of the determinant $\left| \begin{array} { c c } \cos \frac { \pi } { 3 } & \sin \frac { \pi } { 6 } \\ \sin \frac { \pi } { 3 } & \cos \frac { \pi } { 6 } \end{array} \right|$ is $\_\_\_\_$ $0$.
Analysis: This examines the rules for computing determinants. $\left| \begin{array} { c c } \cos \frac { \pi } { 3 } & \sin \frac { \pi } { 6 } \\ \sin \frac { \pi } { 3 } & \cos \frac { \pi } { 6 } \end{array} \right| = \cos \frac { \pi } { 3 } \cos \frac { \pi } { 6 } - \sin \frac { \pi } { 3 } \sin \frac { \pi } { 6 } = \cos \frac { \pi } { 2 } = 0$
(5 points) The equation of the tangent line to the curve $y = x ^ { 3 } - 2 x + 1$ at the point $(1,0)$ is
4. The value of the determinant $\left| \begin{array} { c c } \cos \frac { \pi } { 3 } & \sin \frac { \pi } { 6 } \\ \sin \frac { \pi } { 3 } & \cos \frac { \pi } { 6 } \end{array} \right|$ is $\_\_\_\_$ $0$.

Analysis: This examines the rules for computing determinants. $\left| \begin{array} { c c } \cos \frac { \pi } { 3 } & \sin \frac { \pi } { 6 } \\ \sin \frac { \pi } { 3 } & \cos \frac { \pi } { 6 } \end{array} \right| = \cos \frac { \pi } { 3 } \cos \frac { \pi } { 6 } - \sin \frac { \pi } { 3 } \sin \frac { \pi } { 6 } = \cos \frac { \pi } { 2 } = 0$