91Ó°ÊÓ

Match each trigonometric function with its right triangle definition. (a) sine (b) cosine (c) tangent (d) cosecant (e) secant (f) cotangent (i) \(\frac{\text { hypotenuse }}{\text { adjacent }}\) (ii) \(\frac{\text { adjacent }}{\text { opposite }}\) (iii) \(\frac{\text { hypotenuse }}{\text { opposite }}\) (iv) \(\frac{\text { adjacent }}{\text { hypotenuse }}\) (v) \(\frac{\text { Opposite }}{\text { hypotenuse }}\) (vi) \(\frac{\text { opposite }}{\text { adjacent }}\)

Evaluate the expression without using a calculator. arcsin 0

Sketch a right triangle corresponding to the trigonometric function of the acute angle \(\boldsymbol{\theta} .\) Use the Pythagorean Theorem to determine the third side and then find the other five trigonometric functions of \(\boldsymbol{\theta}\). $$\tan \theta=\frac{4}{5}$$

A ladder that is 20 feet long leans against the side of a house. The angle of elevation of the ladder is \(80^{\circ} .\) Find the height from the top of the ladder to the ground.

Sketch each angle in standard position. (a) \(270^{\circ}\) (b) \(120^{\circ}\)

Sketch the graph of the function. (Include two full periods.) $$y=2 \sec 3 x$$

A Global Positioning System satellite orbits 12,500 miles above Earth's surface (see figure). Find the angle of depression from the satellite to the horizon. Assume the radius of Earth is 4000 miles.

Determine two coterminal angles (one positive and one negative) for each angle. Give your answers in degrees. (a) \(120^{\circ}\) (b) \(-420^{\circ}\)

Sketch the graphs of \(f\) and \(g\) in the same coordinate plane. (Include two full periods.) $$\begin{aligned} &f(x)=-2 \sin x\\\ &g(x)=4 \sin x \end{aligned}$$

During takeoff, an airplane's angle of ascent is \(18^{\circ}\) and its speed is 275 feet per second. (a) Find the plane's altitude after 1 minute. (b) How long will it take for the plane to climb to an altitude of 10,000 feet?