# Arctangent - practice problems

The arctangent is the inverse function of the tangent function. It is usually denoted arctan z or arctg z; in the English literature, ATAN(z) or tan-1 z is also used. There is also a function atan2 with two arguments, y and x atan2(y,x) = arctg y/x, just that it is also defined for x=0 and in all quadrants of the resulting angle.Direction: Solve each problem carefully and show your solution in each item.

#### Number of problems found: 81

- A boy 5

A boy starts at A and walks 3km east to B. He then walks 4km north to C. Find the bearing of C from A. - Subtract polar forms

Solve the following 5.2∠58° - 1.6∠-40° and give answer in polar form - Let z 2

Let z = 2 - sqrt(3i). Find z^{6}and express your answer in rectangular form. if z = 2 - 2sqrt(3 i) then r = |z| = sqrt(2 ^ 2 + (- 2sqrt(3)) ^ 2) = sqrt(16) = 4 and theta = tan -2√3/2=-π/3 - Determine 83083

A 6.5-meter-long ladder rests against a vertical wall. Its lower end rests on the ground 1.6 meters from the wall. Determine how high the top of the ladder reaches and at what angle it rests against the wall.

- Difference 83079

On the traffic sign that informs about the road's gradient, the figure is 6.7%. Determine the slope angle of the path. What height difference is covered by the car that traveled 2.8 km on this road? - Calculate 82567

The volume of a cuboid with a square base is 64 cm^{3}, and the body diagonal deviation from the base's plane is 45 degrees. Calculate its surface area. - Coefficient 82566

What is the maximum angle at which the tram can go downhill to still be able to stop? The coefficient of shear friction is f =0.15. - Trapezoid 82216

Given is an isosceles trapezoid ABCD with bases 10 cm and 14 cm. The height of the trapezoid is 6 cm. Determine the interior angles of the trapezoid. - Calculate 81950

The tangent of the angle formed by the adjacent sides of the triangle ABC (side a=29 m, b = 40 m) equals 1.05. Calculate the area of that triangle.

- Elevation 80869

We can see the top of the tower standing on a plane from a certain point A at an elevation angle of 39° 25''. If we come towards its foot 50m closer to place B, we can see the top of the tower from it at an elevation angle of 56° 42''. How tall is the tow - Elevation 80866

Find the height of the tower when the geodetic measured two angles of elevation α=34° 30'' and β=41°. The distance between places AB is 14 meters. - In the desert

A man wondering in the desert walks 5.7 miles in the direction S 26° W. He then turns 90° and walks 9 miles in the direction N 49° W. At that time, how far is he from his starting point, and what is his bearing from his starting point? - Crosswind

A plane is traveling 45 degrees N of E at 320 km/h when it comes across a current from S of E at 115 degrees of 20 km/h. What are the airplane's new course and speed? - Instantaneous 76754

For a dipole, calculate the complex apparent power S and the instantaneous value of the current i(t), given: R=10 Ω, C=100uF, f=50 Hz, u(t)= square root of 2, sin( ωt - 30 °). Thanks for any help or advice.

- ABS, ARG, CONJ, RECIPROCAL

Let z=-√2-√2i where i2 = -1. Find |z|, arg(z), z* (where * indicates the complex conjugate), and (1/z). Where appropriate, write your answers in the form a + i b, where both a and b are real numbers. Indicate the positions of z, z*, and (1/z) on an Argand - Big tower

From a tower 15 meters high and 30 meters away from the river, the width of the river appeared at an angle of 15°. How wide is the river in this place? - Building 67654

The 15 m high building is 30 m away from the river bank. The river's width can be seen from the roof of this building at an angle of 15 °. How wide is the river? - Horizontal 66434

The lower station of the cable car in Smokovec is at an altitude of 1025m, and the upper station at Hrebienk is at an altitude of 1272m. Calculate the climb of the cable car if the horizontal distance between the slopes is 1921m. - Hypotenuse and center

Point S is the center of the hypotenuse AB of the right triangle ABC. Calculate the area of triangle ABC if the line on the hypotenuse is 0.2 dm long and if angle ∢ACS is 30°.

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