Give the complement and supplement of each angle.

1. \(40^{\circ}\)

2. \(110^{\circ}\)

3. \(\theta\)

The hypotenuse of a right triangle is five. If the two legs are given by two consecutive integers, find the length of the two legs.

The vertical rise of the Forest Double chair lift is \(1,170\) feet and the length of the chair lift is \(5,750\) feet. To the nearest foot, find the horizontal distance covered by a person riding in the lift.

If the shortest side of a \(30^{\circ}-60^{\circ}-90^{\circ}\) triangle is \(5\), find the other two sides.

A ladder is leaning against a wall. The top of the ladder is \(4\) feet above the ground and the bottom of the ladder makes an angle of \(60^{\circ}\) with the ground. How long is the ladder, and how far from the wall is the bottom of the ladder?

A \(10\)-foot rope connects the top of a tent pole to the ground. If the rope makes an angle of \(45^{\circ}\) with the ground, find the length of the tent pole.

Graph the ordered pairs \((-1,3), (2,5), (0,0), (0,-3),\) and \((4,0)\).

Graph \(y=-\displaystyle\frac{1}{3}x\)

Find the \(x\)- and \(y\)-intercepts for \(3x-2y=6\), and graph.

Graph the equation \(y=x^2\).

Graph: \(y=x^2-3\)

Sketch \(x^2+y^2=9\)

If \((x-1)^2 +(y+3)^2=4\) find the center, radius, and graph the circle.

Find the distance between the points \((-1,5)\) and \((2,1)\).

Find the distance from the origin to the point \((x,y)\).

Draw an angle of \(45^{\circ}\) in standard position and find a point on the terminal side.

Draw \(-90^{\circ}\) in standard position and find the two positive angles and two negative angles that are coterminal with \(-90^{\circ}\).

Find the six trigonometric functions of \(\theta\) if \(\theta\) is in standard position and the point \((-2,3)\) is on the terminal side of \(\theta\).

Find the sine and cosine of \(45^{\circ}\).

Find the six trigonometric functions of \(270^{\circ}\).

If \(\sin{\theta}=-\displaystyle\frac{5}{13}\), and \(\theta\) terminates in quadrant III, find \(\cos{\theta}\) and \(\tan{\theta}\).

If \(\sin{\theta}=\displaystyle\frac{3}{5}\), then \(\csc{\theta}=\)?

If \(\cos{\theta}=-\displaystyle\frac{\sqrt{3}}{2}\), then \(\sec{\theta}=\)?

If \(\tan{\theta}=2\), then \(\cot{\theta}=\)?

If \(\csc{\theta}=a\) then \(\sin{\theta}=\)?

If \(\sec{\theta}=1\), then \(\cos{\theta}=\)?

If \(\cot{\theta}=-1\), then \(\tan{\theta}=\)?

If \(\sin{\theta}=-\displaystyle\frac{3}{5}\) and \(\cos{\theta}=\displaystyle\frac{4}{5}\), find \(\tan{\theta}\) and \(\cot{\theta}\).

If \(\sin{\theta}=\displaystyle\frac{3}{5}\), then \(\sin^2{\theta}=\)?

If \(\cos{\theta}=-\displaystyle\frac{1}{2}\), then \(\cos^3{\theta}=\)?

If \(\sin{\theta}=\displaystyle\frac{3}{5}\) and \(\theta\) terminates in QII, find \(\cos{\theta}\) and \(\tan{\theta}\).

If \(\cos{\theta}=\displaystyle\frac{1}{2}\) and \(\theta\) terminates in QIV, find the remaining trigonometric ratios for \(\theta\).

Write \(\sec\theta\tan\theta\) in terms of \(\sin\theta\) and \(\cos\theta\), and then simplify.

Add \(\displaystyle\frac{1}{\sin\theta}+\displaystyle\frac{1}{\cos\theta}\).

Multiply \((\sin\theta +2)(\sin\theta -5)\).

Show that the following statement is true by transforming the left side into the right side. \[\cos\theta\tan\theta=\sin\theta\]