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.

solve 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

Give 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

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

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 =

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.

Solve 3 cos(x) - 11 cos(x) - 4 = 0 for all solutions 0 < x < 2π

Solve 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

Solve sin² (t) = 8 cos(t) for all solutions 0 < t < 2π t =

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

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.

Simplifysec(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) =

Solve 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°

What is the amplitude of the following function? y = 0.379 cos x

Find the horizontal shift. y = sin(4θ - pi/2)

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?

A 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[?]°