Goniometry and trigonometry - practice problems
Number of problems found: 457
- Cis notation
Evaluate multiplication of two complex numbers in cis notation: (6 cis 120°)(4 cis 30°) Write result in cis and Re-Im notation. - Trigonometry
Is true equality? sin(x +13 π)= sin(x) - Cotangent
If the angle α is acute, and cotan α = 1/3. Determine the value of sin α, cos α, tg α. - 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
- Altitude angles
Cities A, B, C lie in one elevation plane. C is 50 km east of B, B is north of A. C is deviated by 50° from A. The plane flies around places A, B, C at the same altitude. When the aircraft is flying around B, its altitude angle to A is 12°. Find the altit - 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 see 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 length of the shortest side, write the result in cm up to two decimal places. - Components 2565
What is the weight of 200 components in the shape of regular decagons with a side of 2 cm if the weight of 1 m² of sheet metal from which they are made is 24 kg? - 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 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? - The rescue helicopter
The rescue helicopter is above the landing site at a height of 180m. The site of the rescue operation can be seen from here at a depth angle of 52° 40 '. How far will the helicopter land from the rescue site? - Rectangle 49153
Rectangle ABCD, whose | AB | = 5cm, | AC | = 8 cm, ∢ | CAB | = 30 °. How long is the other party and what is its area? - A chord
In a circle of radius 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. - Steps
Find the height between the two floors if you know that the number of steps between the two floors is 18, the gradient is 30º, and the length of the step is 28.6 cm. Report the result in centimeters to the nearest centimeter. - Elevation angles
From the endpoints of the base 240 m long and inclined at an angle of 18° 15 ', the top of the mountain can be seen at elevation angles of 43° and 51°. How high is the mountain? - Reflector
Circular reflector throws light cone with a vertex angle 49° and is on 33 m height tower. The axis of the light beam has with the axis of the tower angle 30°. What is the maximum length of the illuminated horizontal plane?
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