# Goniometry and trigonometry - practice problems

#### Number of problems found: 485

- Cis notation

Evaluate multiplication of two complex numbers in cis notation: (6 cis 120°)(4 cis 30°) Write the result in cis and Re-Im notation. - Cotangent

If the angle α is acute, and cotan α = 1/3. Determine the value of sin α, cos α, and tan α. - Trigonometry

Is true equality? sin(x +13 π)= sin(x) - Sinus

Determine the smallest integer p for which the equation 4 sin x = p has no solution. - Modulus and argument

Find the mod z and argument z if z=i - Perpendicular 17423

According to the map, the scouts were supposed to proceed through the forest perpendicular to its straight edge, where the goal was 3 km away from the starting point. They already deviated from the correct direction by 5° at the start. How far from the ta - Altitude angles

Cities A, B, and C lie in one elevation plane. C is 50 km east of B, and B is north of A. C is deviated by 50° from A. The plane flies around places A, B, and C at the same altitude. When the aircraft is flying around B, its altitude angle to A is 12°. Fi - Altitude angle

In complete winds-free weather, the balloon took off and remained standing exactly above the place from which it took off. It is 250 meters away from us. How high did the balloon fly when we saw it at an altitude angle of 25°? - Three pillars

On a straight road, three pillars are 6 m high at the same distance of 10 m. At what angle of view does Vlado see each pillar if it is 30 m from the first and his eyes are at 1.8 m high? - Inner angles

The inner angles of the triangle are 30°, 45°, and 105° and its longest side is 10 cm. Calculate the shortest side length, and write the result in cm up to two decimal places. - (connecting 45471

There are 12 seats evenly distributed on the children's carousel in the shape of a circle. How long is the arm of the carousel (connecting the center of the carousel to the seat) if the distance between the two seats is 1.5m? - Embankment 7879

An embankment 7.5 m high should be built on the horizontal plane. The width of the upper surface of the embankment is 2.9 m, and the slope is 35 °. What will be the lower width of the embankment? - Which

Which of the following numbers most accurately area of a regular decagon with side s = 2 cm? (A) 9.51 cm² (B) 20 cm² (C) 30.78 cm² (D) 31.84 cm² (E) 32.90 cm^{2} - A ship

A ship has been spotted by two lighthouses, A and B, as shown in the figure. What is the distance from the ship to Lighthouse A to the nearest tenth? Figure - the distance between lighthouses A and B is 40 nautical miles. From A is seen in view angle 57° - Observation 17433

The aircraft flying just above point A can be seen from observation B, 2,400 meters away from point A, at an altitude of 52°30'. How high does the plane fly? - Carousel for children

There are 5 seats evenly distributed on the children's carousel in the shape of a circle. What kind the arm of the carousel (connecting the center of the carousel to the seat) is long if the distance between with two seats is 1.2m? - The rescue helicopter

The rescue helicopter is above the landing site at a height of 180m. The rescue operation site can be seen from here at a depth angle of 52°40'. How far will the helicopter land from the rescue site? - Components 2565

The component has the shape of regular decagons with a side of 2 cm. Its material weight of 1 m² of sheet metal is 24 kg. What is the weight of 200 components? - A chord

In a circle radius of 6 cm, a chord is drawn 3 cm from the center. Calculate the angle subtended by the cord at the center of the circle Hence find the length of the minor arc cut off by the chord. - Bridge across the river

The width of the river is 89 m. For terrain reasons, the bridge deviates from a common perpendicular to both banks by an angle of 12° 30 '. Calculate how many meters the bridge is longer than the river.

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