Goniometry and trigonometry - practice problems - page 2 of 32
Trigonometric functions model periodic phenomena such as waves, oscillations, and circular motion. Inverse trigonometric functions solve for angles given ratios. This field is essential for navigation, engineering, physics, architecture, and any application involving angles, rotations, or periodic behavior.Number of problems found: 632
- Three 235
Three houses form a triangular shape. House A is 50 feet from house C and house B is 60 feet from house C. The measure is angle ABC is 45 degrees. Draw a picture and find the distance between A and B. - Subtract polar forms
Solve the following 5.2∠58° - 1.6∠-40° and give answer in polar form - A tree 3
A tree breaks due to a storm and the broken part bends so that the top of the tree touches the ground at an angle of 30°. The distance from the foot of the tree to the point where the top touches the ground is 8 m. Find the original height of the tree. - Rhombus 36
Rhombus ABCD with side 8 cm long has diagonal BD 11.3 cm long. Find angle DAB. - A lighthouse
A lighthouse overlooks a bay, and it is 77 meters high. From the top, the lighthouse keeper can see a yacht southward at an angle of depression of 32 degrees and another boat eastward at an angle of 25 degrees. What is the distance between the boats? - Piece of a wire
A piece of wire is bent into the shape of a triangle. Two sides have lengths of 24 inches and 21 inches. The angle between these two sides is 55°. What is the length of the third side to the nearest hundredth of an inch? A: The length of the third side is - Cplx sixth power
Let z = 2 - sqrt(3i). Find z6 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 - A triangle 7
A triangle lot has the dimensions a=15 m, b=10 m, and c=20 m. What is the measure of the angle between the sides of b and c? - Cosine - legs
Using the law of cosines, find the measurement of leg b if the givens are β=20°, a=10, and c=15. - Conjugate coordinates
If the rectangular conjugate of the polar vector 12 angle 35 degrees is equal to x+yi, find the sum of x and y. - The apothem
The apothem of a regular hexagon is 5√3 inches. Find one of its sides and area. - ABCD rhombus
ABCD is a rhombus with sides of 10.5 cm. If the length of diagonal AC = 15.8 cm, use the cosine rule to: a. calculate the length of diagonal BD to the nearest centimetre, b. find the angles of the rhombus to the nearest degree. - Building shadow
When the Sun's altitude is 30° above the horizontal, find the length of the shadow cast by a 50 m high building. - A boy 5
A boy starts at A and walks 3 km east to B. He then walks 4 km north to C. Find the bearing of C from A. - Vertical components
Find the horizontal and vertical components of the vector which has a magnitude of 750 as shown in the figure. - Angle and slope
Find the angle between the x-axis and the line joining the points (3, −1) and (4, −2). - Trigonometric fx
When an acute angle φ is in the standard position, its terminal side passes through point P (1,3). Find trigonometric functions of angle θ : sin φ, cos φ, tan φ, cotan φ. - 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) - Observatories A,B
The target C is observed from two artillery observatories, A and B, 296 m apart. At the same time, angle BAC = 52°42" and angle ABC = 44°56". Calculate the distance of the target C from observatory A.
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