Maths - Multiple Trig Solutions

What’s the easiest way to answer a question about mutliple trigonometry solutions?

After how many degrees does $\sin(\theta)$ repeat?

After how many degrees does $\cos(\theta)$ repeat?

After how many degrees does $\tan(\theta)$ repeat?

When drawing a $\tan$ graph, what should you sketch first?

Where are the asymptotes on a $\tan$ graph, in degrees?

What is the value of $\sin$ at the origin?

What is the value of $\cos$ at the origin?

What is the value of $\tan$ at the origin?

How could you write $\tan\theta$ in terms of $\sin$ and $\cos$?

If $\cos 90^{\circ}$ is zero, why is $\tan 90^{\circ}$ undefined?

This diagram shows a triangle where $\theta$ is approaching $0$. What is the value of $\cos\theta$ approaching?

This diagram shows a triangle where $\theta$ is approaching $0$. What is the value of $\sin\theta$ approaching?

What proportion of the hypotenuse is the opposite side?

If your calculator gives you $x$ as a solution to $\sin^{-1}$, what are the three other solutions?

If your calculator gives you $x$ as a solution to $\cos^{-1}$, what are the three other solutions?

$\cos^{-1}$ has solutions $x$ and $360 - x$. Because $\cos\theta = \cos-\theta$, what are the other two solutions?

If your calculator gives you $x$ as a solution to $\tan^{-1}$, what are the other two solutions?

How could you find one solution of $\sin(2\theta) = 0.1$?

How could you find one solution of $\sin(\theta + 30^{\circ}) = 0.1$?