Trigonometric equations Questions and Answers
![Sketch the graph the function y = csc(22) over the interval [0, π). Label the x and y-axis so that the important characteristics of the graph are illustrated clearly.](https://media.kunduz.com/media/sug-question/raw/84513498-1657990393.3918169.jpeg?w=256)
Math - Others
Trigonometric equationsSketch the graph the function y = csc(22) over the interval [0, π). Label the x and y-axis so that the important characteristics of the graph are illustrated clearly.
![solve sin(x) = -0.54 on 0<x<2π
A =
B =
Give answer accurate to 3 decimal
places](https://media.kunduz.com/media/sug-question/raw/84481066-1657981736.2188847.jpeg?w=256)
Math - Others
Trigonometric equationssolve sin(x) = -0.54 on 0<x<2π
A =
B =
Give answer accurate to 3 decimal
places
![solve 4sin(4x) = 4 for smallest
positive solutions A and B
with A<B
A =
B =
Give answer accurate to two
decimal places](https://media.kunduz.com/media/sug-question/raw/84481226-1657981697.0024161.jpeg?w=256)
Math - Others
Trigonometric equationssolve 4sin(4x) = 4 for smallest
positive solutions A and B
with A<B
A =
B =
Give answer accurate to two
decimal places
![Give the equation y=4sin(5πx/4-25π/4)+8
Amplitude=
Period=
horizontal shift =
Midline is y=](https://media.kunduz.com/media/sug-question/raw/84481366-1657981655.2544773.jpeg?w=256)
Math - Others
Trigonometric equationsGive the equation y=4sin(5πx/4-25π/4)+8
Amplitude=
Period=
horizontal shift =
Midline is y=
![Find all solutions of the equation.
2 cos x-1=0](https://media.kunduz.com/media/sug-question/raw/84395830-1657807872.7290347.jpeg?w=256)
![Show directly that the given functions are linearly dependent on the real line. That is, find a nontrivial linear combination of the following functions that vanishes identically
f(x)=23, g(x)=5 sin^2x, h(x) = 6 cos²x
Enter the non trivial linear combination
(30)(23) +(6sin^2x) +(____+6 cos²x)=0](https://media.kunduz.com/media/sug-question/raw/84477723-1657731004.3558028.jpeg?w=256)
Math - Others
Trigonometric equationsShow directly that the given functions are linearly dependent on the real line. That is, find a nontrivial linear combination of the following functions that vanishes identically
f(x)=23, g(x)=5 sin^2x, h(x) = 6 cos²x
Enter the non trivial linear combination
(30)(23) +(6sin^2x) +(____+6 cos²x)=0
![A bicycle wheel has radius R. Let P be a point on the spoke of a wheel at a distance d from the center of the wheel. The wheel begins to roll to the right along the the x-axis. The curve traced out by P is given by the following parametric equations:
(x(θ) = 11θ - 5 sin (θ)
y(θ) = 11 - 5 cos (θ)
What must we have for R and d?
R=
d =](https://media.kunduz.com/media/sug-question/raw/84395546-1657617306.2280035.jpeg?w=256)
Math - Others
Trigonometric equationsA bicycle wheel has radius R. Let P be a point on the spoke of a wheel at a distance d from the center of the wheel. The wheel begins to roll to the right along the the x-axis. The curve traced out by P is given by the following parametric equations:
(x(θ) = 11θ - 5 sin (θ)
y(θ) = 11 - 5 cos (θ)
What must we have for R and d?
R=
d =
![A hot-air balloon is rising vertically 14 ft/sec while the wind is blowing horizontally at 4 ft/sec. Find the speed v of the balloon and the angle 8 it makes with the
horizontal.
The balloon's sphed is ft/sec, and it is rising at an angle of to the horizontal.](https://media.kunduz.com/media/sug-question/raw/84333655-1657400577.3669467.jpeg?w=256)
Math - Others
Trigonometric equationsA hot-air balloon is rising vertically 14 ft/sec while the wind is blowing horizontally at 4 ft/sec. Find the speed v of the balloon and the angle 8 it makes with the
horizontal.
The balloon's sphed is ft/sec, and it is rising at an angle of to the horizontal.
![Solve 3 cos(x) - 11 cos(x) - 4 = 0 for all solutions 0 < x < 2π](https://media.kunduz.com/media/sug-question/raw/84230193-1657040068.8583367.jpeg?w=256)
![Solve sin (3x) cos(5x) - cos(3x) sin(5x)=-0.35 for the smallest positive solution.
x=](https://media.kunduz.com/media/sug-question/raw/84228785-1657035258.5221982.jpeg?w=256)
Math - Others
Trigonometric equationsSolve sin (3x) cos(5x) - cos(3x) sin(5x)=-0.35 for the smallest positive solution.
x=
![Solve 6 sin(π/3 x) =4 for the four smallest positive solutions](https://media.kunduz.com/media/sug-question/raw/84228436-1657035181.2209458.jpeg?w=256)
![Solve sin² (t) = 8 cos(t) for all solutions 0 < t < 2π
t =](https://media.kunduz.com/media/sug-question/raw/84228845-1657035094.3449018.jpeg?w=256)
![Solve sec(4x) - 8 = 0 for the four smallest positive solutions
x=
Give your answers accurate to at least two decimal places, as a list separated by commas](https://media.kunduz.com/media/sug-question/raw/84229054-1657035012.4290686.jpeg?w=256)
Math - Others
Trigonometric equationsSolve sec(4x) - 8 = 0 for the four smallest positive solutions
x=
Give your answers accurate to at least two decimal places, as a list separated by commas
![Find c if a = 2.18 mi, b = 3.45 mi and angle C = 40.2 degrees.
Enter c rounded to 3 decimal places.
C=
Assume angle A is opposite side a, angle B is opposite side b, and angle C is opposite side c.](https://media.kunduz.com/media/sug-question/raw/84223810-1657019044.0334597.jpeg?w=256)
Math - Others
Trigonometric equationsFind c if a = 2.18 mi, b = 3.45 mi and angle C = 40.2 degrees.
Enter c rounded to 3 decimal places.
C=
Assume angle A is opposite side a, angle B is opposite side b, and angle C is opposite side c.
![Simplifysec(t) - cos(t)/ sin(t). to a single trig function with no fractions.](https://media.kunduz.com/media/sug-question/raw/84212238-1657017516.3792453.jpeg?w=256)
Math - Others
Trigonometric equationsSimplifysec(t) - cos(t)/ sin(t). to a single trig function with no fractions.
![Write the sum as a product:
cos(17.6t) + cos(11.2t) =](https://media.kunduz.com/media/sug-question/raw/84212319-1657016929.462582.jpeg?w=256)
![Solve 8 sin(4x) = 4 for all solutions in the interval (0, 2pi). Give your answers accurate to at least two
decimal places.](https://media.kunduz.com/media/sug-question/raw/84212325-1657016894.9197092.jpeg?w=256)
Math - Others
Trigonometric equationsSolve 8 sin(4x) = 4 for all solutions in the interval (0, 2pi). Give your answers accurate to at least two
decimal places.
![Find the value of the given trigonometric function by finding the reference angle a and attaching the proper sign.
tan 306°](https://media.kunduz.com/media/sug-question/raw/84222558-1657016432.4079626.jpeg?w=256)
Math - Others
Trigonometric equationsFind the value of the given trigonometric function by finding the reference angle a and attaching the proper sign.
tan 306°
![What is the amplitude of the following function?
y = 0.379 cos x](https://media.kunduz.com/media/sug-question/raw/84228109-1657014665.645796.jpeg?w=256)
Math - Others
Trigonometric equationsWhat is the amplitude of the following function?
y = 0.379 cos x
![Find the horizontal shift.
y = sin(4θ - pi/2)](https://media.kunduz.com/media/sug-question/raw/84228382-1657014603.7194762.jpeg?w=256)
![A sine function has an amplitude of 4, period of 2π, horizontal shift of -3π,, and vertical shift of 1. What is the y-value of the positive function at x = π,/2?](https://media.kunduz.com/media/sug-question/raw/84228585-1657012885.2190173.jpeg?w=256)
Math - Others
Trigonometric equationsA sine function has an amplitude of 4, period of 2π, horizontal shift of -3π,, and vertical shift of 1. What is the y-value of the positive function at x = π,/2?
![A sound wave has an equation y = 7 sin(58πt) where t = time in seconds What is its frequency?
[?] cycles/second](https://media.kunduz.com/media/sug-question/raw/84229574-1657012607.9946406.jpeg?w=256)
Math - Others
Trigonometric equationsA sound wave has an equation y = 7 sin(58πt) where t = time in seconds What is its frequency?
[?] cycles/second
![Express the following as a function of a single angle.
sin 340° cos 120° - cos 340° sin 120°
sin[?]°](https://media.kunduz.com/media/sug-question/raw/84162397-1656959219.5045443.jpeg?w=256)
Math - Others
Trigonometric equationsExpress the following as a function of a single angle.
sin 340° cos 120° - cos 340° sin 120°
sin[?]°