Use the fundamental identities to simplify the expression. There is more than one correct form of each answer. $\csc \phi \tan \phi+\sec \phi$

The bearing from the Pine Knob fire tower to the Colt Station fire tower is N 65$^{\circ}$ E and the two towers are 30 kilometers apart. A fire spotted by rangers in each tower has a bearing of N 80$^{\circ}$ E from Pine Knob and S 70$^{\circ}$ E from Colt Station (see figure). Find the distance of the fire from each tower.

Confirm the results of parts (a) and (b) algebraically.

$$2+\cos ^2 x-3 \cos ^4 x=\sin ^2 x\left(3+2 \cos ^2 x\right)$$

use a graphing utility to approximate the solutions (to three decimal places) of the equation in the interval 0, 2π). 2 sin x + cox x = 0

find the exact value of the trigonometric expression given that sin u = 5/13 and cos v = -3/5. (Both u and v are in Quadrant II.) cot(u + v)

(a) Use a graphing utility to graph each side of the equation 2 + cos$^2$x - 3 cos$^4$x = sin$^2$x(3 + 2 cos$^2$x) to determine whether the equation is an identity, (b) use the table feature of the graphing utility to determine whether the equation is an identity, and (c) confirm the results of parts (a) and (b) algebraically.

A pilot has just started on the glide path for landing at an airport with a runway of length 9000 feet. The angles of depression from the plane to the ends of the runway are $17.5^{\circ}$ and $18.8^{\circ}$. Find the altitude of the plane when the pilot begins the descent.

Use the table feature of a graphing utility to determine whether the equation is an identity.

$$2+\cos ^2 x-3 \cos ^4 x=\sin ^2 x\left(3+2 \cos ^2 x\right)$$

use the fundamental identities to simplify the expression. sin tan cos 

find the exact value of the trigonometric expression given that sin u = - 7/25 and cos v = - 4/5. (Both u and v are in Quadrant III.) csc(u - v)

A pilot has just started on the glide path for landing at an airport with a runway of length 9000 feet. The angles of depression from the plane to the ends of the runway are $17.5^{\circ}$ and $18.8^{\circ}$. Find the ground distance the plane must travel until touching down.

A pilot has just started on the glide path for landing at an airport with a runway of length 9000 feet. The angles of depression from the plane to the ends of the runway are $17.5^{\circ}$ and $18.8^{\circ}$. Find the air distance the plane must travel until touching down on the near end of the runway.

Find the x-intercepts of the graph of y = sec$^4\left(\frac{\pi x}{8}\right)$ - 4.

A pilot has just started on the glide path for landing at an airport with a runway of length 9000 feet. The angles of depression from the plane to the ends of the runway are $17.5^{\circ}$ and $18.8^{\circ}$. Draw a diagram that visually represents the situation.