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.
If the angle α is acute, and cotan α = 1/3. Determine the value of sin α, cos α, and tan α.
Is true equality? sin(x +13 π)= sin(x)
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: sin4 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 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 cm2
- 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?
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?
Most natural application of trigonometry and trigonometric functions is a calculation of the triangles. Common and less common calculations of different types of triangles offers our triangle calculator. Word trigonometry comes from Greek and literally means triangle calculation.