In a right triangle, define \(\sin\theta\) using side lengths.

On the unit circle, what are the coordinates of the point corresponding to angle \(\theta\)?

Find \(\tan\theta\) if the opposite side is \(6\) and the adjacent side is \(8\).

State the period of \(\sin x\) and \(\tan x\).

If \(\sin\theta=\frac{5}{13}\) and \(\cos\theta=\frac{12}{13}\), find \(\tan\theta\).

Find \(\sec\theta\) when \(\cos\theta=-\frac14\).

A point on the unit circle is \(\left(-\frac35,\frac45\right)\). Find \(\sin\theta\), \(\cos\theta\), and \(\tan\theta\).

Evaluate \(\sin\left(\frac{5\pi}{2}\right)\) using periodicity.

A right triangle has hypotenuse \(10\) and side adjacent to \(\theta\) equal to \(6\). Find \(\cos\theta\) and \(\sec\theta\).

For \(\theta=\pi\), find \(\sin\theta\), \(\cos\theta\), and \(\tan\theta\).

Explain why \(\tan\left(\frac\pi2\right)\) is undefined.

A force of magnitude \(20\) N makes angle \(\theta\) with the positive \(x\)-axis. Write its horizontal and vertical components using trig functions, and evaluate them if \(\cos\theta=0.6\) and \(\sin\theta=0.8\).

Find all \(x\) in \([0,2\pi)\) for which \(\sin x=0\).

Find all \(x\) in \([0,2\pi)\) for which \(\cos x=0\).

For which real \(x\) is \(\sec x\) undefined?

For which real \(x\) is \(\cot x\) undefined?

A student claims \(\sin(x+\pi)=\sin x\) because sine is periodic. Correct the claim.

Show from the unit circle that \(\sin^2\theta+\cos^2\theta=1\).

Explain why tangent has period \(\pi\) even though sine and cosine each have period \(2\pi\).

A moving point on a unit circle has position \((\cos t,\sin t)\), where \(t\) is in radians. Explain why each coordinate is bounded between \(-1\) and \(1\), and identify when the horizontal coordinate is \(1\).