#1
In a right triangle, if the length of the side opposite the right angle is 5 and the length of one of the other sides is 10, what is the sine of the angle opposite the side of length 10?
#2
Which of the following trigonometric ratios represents the relationship between the side adjacent to an acute angle in a right triangle and the hypotenuse?
#3
In a right triangle, if one acute angle measures 45 degrees, what is the value of the tangent of that angle?
#4
Which trigonometric ratio is equal to the reciprocal of sine?
#5
If sin(θ) = 0.6 and θ is an acute angle, what is the value of cos(θ)?
#6
Which of the following trigonometric ratios is equal to the reciprocal of cosine?
#7
In a right triangle, if one acute angle measures 30 degrees, what is the cosine of that angle?
#8
A pendulum swings back and forth with a period of 2 seconds. If the length of the pendulum is 1 meter, what is the angular frequency of the pendulum's motion in radians per second?
#9
What is the period of the function y = 2sin(3x) + 1?
#10
A wheel with a radius of 0.5 meters rotates at a constant angular speed of 2 radians per second. What is the linear speed of a point on the edge of the wheel in meters per second?
#11
What is the amplitude of the function y = 4sin(2x) + 3?
#12
A point moves along the circumference of a circle with a radius of 2 meters at a constant linear speed of 3 meters per second. What is the angular speed of the point in radians per second?
#13
A particle moves along the x-axis with simple harmonic motion described by the equation x(t) = 3cos(2t + π/3), where x(t) is the position of the particle at time t. What is the amplitude of the motion?
#14
A ladder is leaning against a wall with the top of the ladder 5 meters above the ground. If the ladder forms a 60-degree angle with the ground, how far is the base of the ladder from the wall?
#15
A Ferris wheel has a diameter of 50 meters and rotates at a rate of 0.1 radians per second. What is the linear speed of a passenger located 20 meters from the center of the Ferris wheel?
#16
A tower casts a shadow 30 meters long on the ground when the angle of elevation of the sun is 45 degrees. What is the height of the tower?
#17