Exam 7: Applications of Trigonometry

Solve. -A ship travels 81 km on a bearing of 29°, and then travels on a bearing of 119° for 164 km. To the nearest kilometer, find the distance from the start to the end of the trip.

Change the polar coordinates to rectangular coordinates (x, y). -(-10, 225°)

Graph the pair of parametric equations in the rectangular coordinate system. -

Solve. -A plane flying a straight course observes a mountain at a bearing of 30.1° to the right of its course. At that time the plane is 6 km from the mountain. A short time later, the bearing to the mountain becomes 40.1°. How far is The plane from the mountain when the second bearing is taken (to the nearest tenth of a km)?

Express the given vector as a linear combination of the unit vectors i and j. --7, 8

Graph the pair of parametric equations with the aid of a graphing calculator. -

Solve the problem. -An airplane flies on a compass heading of 90.0° at 480 mph. The wind affecting the plane is blowing from 295° at 23.0 mph. What is the true course and ground speed of the airplane? Round results to an appropriate number Of significant digits.

Change the polar coordinates to rectangular coordinates (x, y). -

Solve the problem. -A basketball player shoots the ball with a velocity of 12.8 ft/s at an angle of 40.8° with the horizontal. To the nearest tenth, find the magnitude of the horizontal component of the resultant vector.

Find the absolute value of the complex number. -4i

State if the vectors a and b are perpendicular, parallel, or neither. If a and b are parallel, state whether they point in the same direction or in opposite directions. -a = 7, 4 , b = 5, 1

Use De Moivre's theorem to simplify the expression. Write the answer in the form a + bi. -

Use De Moivre's theorem to simplify the expression. Write the answer in the form a + bi. -

Determine the number of triangles with the given parts. -a = 4, b = 7, c = 11

Solve. -A ranger in fire tower A spots a fire at a direction of 40°. A ranger in fire tower B, which is 28 miles directly east of tower A, spots the same fire at a direction of 116°. How far from tower A is the fire? Round to the nearest Mile.

For the given polar equation, write an equivalent rectangular equation. -

For the given rectangular equation, write an equivalent polar equation. -2x + 3y = 6

Perform the operation using trigonometric form. Write the answer in the form a + bi -

Write the complex number in the form a + bi. -4(cos -135° + i sin -135°)

For the given polar equation, write an equivalent rectangular equation. -