Sine - practice problems
The sine function is a fundamental trigonometric ratio relating an angle in a right triangle to the ratio of the opposite side to the hypotenuse. Denoted as sin(θ), it varies between -1 and 1 for all angles. The sine function extends beyond right triangles through the unit circle definition and describes periodic oscillations. Its graph is a smooth wave with period 2π, making it essential for modeling cyclical phenomena like sound waves, tides, and alternating current. The sine function relates to the cosine through complementary angles: sin(θ) = cos(90° - θ). Understanding sine is crucial for solving triangles, analyzing waves, and advanced calculus applications.Number of problems found: 327
- Triangle 97
Triangle DEF with Ê=40°, F=90° EF = 45mm. Measure DE. - Vertical components
Find the horizontal and vertical components of the vector which has magnitude 750 as shown in the following figure. - Angle of inclination
Find the angle of inclination of a ramp that rise for 80 cm and is 200 cm long. - Triangle 90
Triangle made by 6 cm 4.5 cm and 7.5 cm. what angles does it make? - A kite 3
A kite is flying at a height of 60 m above the ground. The string attached to the kite is temporarily tied to a point on the ground. The inclination of the string with the ground is 60°. Find the length of the string, assuming that there is no slack in th - The tent 3
The top of a 1.3 meters tall tent is tethered to the ground by a cable. The cable makes a 37 degrees angle with the ground. Find the cable length. - An electrician 7
An electrician has to repair an electric fault on a pole 4 meters in height. He needs to reach a point 1 m below the top. What should be the length of the ladder that he could use, when inclined at an angle 60° to the horizontal? - X-triangle
Find the length of the x segment in the given triangle drawings. - 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. - 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. - A right
A right triangle has side lengths a=3, b=5, and c=4, as shown below. Use these lengths to find tan x, sin x, and cos x. - Subtract polar forms
Solve the following 5.2∠58° - 1.6∠-40° and give answer in polar form - 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. - 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 - Tunnel - quadrilateral How long will the tunnel AB be, distances AD=35 m, DC=120 m, CB=85 m, and angles ADC=105 degrees and BCD=71 degrees. ABCD is a quadrilateral.
- Parallelogram 44
Parallelogram ABCD has an area of 32 cm2, lABl=8cm, lBCl=5cm. Calculate the sizes of its interior angles. - Determine the surface area
Find the surface area of a cone of height 30 cm whose side makes an angle of 60° with the base plane. - Mirror
The dimensions of the mirror are 750mm x 700mm, the mirror should be tilted 8° from the wall. How many cm must it be tilted from the wall? - Quadrilateral - irregular
Find the length of the side d = |AD| in quadrilateral ABCD: a= 35m, b= 120m, c=85m, angle ABC = 105 degrees, angle BCD= 72 degrees - Unit circle
In the Cartesian coordinate system, a unit circle is given on which points A and B lie. Point O is the origin and has coordinates (0,0) and point B has coordinates (1,0). The size of angle BOA is 151°. Determine the x-coordinate of point A.
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