# Goniometry and trigonometry - practice problems

#### Number of problems found: 546

- 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 - A radio antenna

Avanti is trying to find the height of a radio antenna on the roof of a local building. She stands at a horizontal distance of 21 meters from the building. The angle of elevation from her eyes to the roof (point A) is 42°, and the angle of elevation from - Entrepreneur 6309

Renting a 1m² advertising board costs €780 per month. A rectangular advertising board has a length of 3 m and its diagonal makes an angle of 34 degrees with the longer side. Calculate how much € an entrepreneur will pay for 4 months of renting a blackboar - Substitution method

Solve a goniometric equation: sin^{4}θ - 1/cos² θ=cos² θ - 2 - 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 - Observation 82708

At the top of the hill, there is a 30-meter-high observation tower. We can see its heel and shelter from a certain point in the valley at elevation angles a=28°30" and b=30°40". How high is the top of the hill above the horizontal plane of the observation - 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°? - 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° - 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 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. - 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? - 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} - 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? - Steeple

We see the church tower from the road at an angle of 52°. When we zoom out to 29 meters away, it can be seen at an angle of 21°. How high is it?

Do you have homework that you need help solving? Ask a question, and we will try to solve it.