Match each equation with its general solution. square cos(Theta )=-1 square cos(Theta )=1 square sin(Theta )=0 square sin(Theta )=1 square sin(Theta )=-1 square cos(Theta )=0 a. Theta =(pi )/(2)+pi k k any integer b. Theta =pi +2pi k k any integer c. Theta =2pi k k any integer d. Theta =(3pi )/(2)+2pi k k any integer e. Theta =pi k k any integer f. Theta =(pi )/(2)+2pi k k any integer

Let's match each equation with its general solution:<br /><br />1. $cos(\Theta )=-1$<br /> - General solution: $\Theta =\pi +2\pi k$ where $k$ is any integer.<br /> - Match: $\square $ $cos(\Theta )=-1$ $\rightarrow$ $\square $ $cos(\Theta )=1$<br /><br />2. $cos(\Theta )=1$<br /> - General solution: $\Theta =2\pi k$ where $k$ is any integer.<br /> - Match: $\square $ $cos(\Theta )=1$ $\rightarrow$ $\square $ $cos(\Theta )=0$<br /><br />3. $sin(\Theta )=0$<br /> - General solution: $\Theta =\pi k$ where $k$ is any integer.<br /> - Match: $\square $ $sin(\Theta )=0$ $\rightarrow$ $\square $ $sin(\Theta )=1$<br /><br />4. $sin(\Theta )=1$<br /> - General solution: $\Theta =\frac {\pi }{2}+2\pi k$ where $k$ is any integer.<br /> - Match: $\square $ $sin(\Theta )=1$ $\rightarrow$ $\square $ $sin(\Theta )=-1$<br /><br />5. $sin(\Theta )=-1$<br /> - General solution: $\Theta =\frac {3\pi }{2}+2\pi k$ where $k$ is any integer.<br /> - Match: $\square $ $sin(\Theta )=-1$ $\rightarrow$ $\square $ $cos(\Theta )=0$<br /><br />6. $cos(\Theta )=0$<br /> - General solution: $\Theta =\frac {\pi }{2}+\pi k$ where $k$ is any integer.<br /> - Match: $\square $ $cos(\Theta )=0$ $\rightarrow$ $\square $ $cos(\Theta )=-1$<br /><br />So the final matches are:<br />$\square $ $cos(\Theta )=-1$ $\rightarrow$ $\square $ $cos(\Theta )=1$<br />$\square $ $cos(\Theta )=1$ $\rightarrow$ $\square $ $cos(\Theta )=0$<br />$\square $ $sin(\Theta )=0$ $\rightarrow$ $\square $ $sin(\Theta )=1$<br />$\square $ $sin(\Theta )=1$ $\rightarrow$ $\square $ $sin(\Theta )=-1$<br />$\square $ $sin(\Theta )=-1$ $\rightarrow$ $\square $ $cos(\Theta )=0$<br />$\square $ $cos(\Theta )=0$ $\rightarrow$ $\square $ $cos(\Theta )=-1$