# Trig

Find the general solution for the equation 4tanx+cotx=5?????? and the steps please? THANYOO!

1. 👍 1
2. 👎 1
3. 👁 646
1. For these I generally like to change everything to sines and cosines

4tanx + cotx = 5
4sinx/cosx + cosx/sinx = 5
(4sin^2x + cos^2x)/sinxcosx = 5
4sin^2x + cos^2x = 5sinxcosx
4sin^2x - 5sinxcosx + cos^2x = 0
(4sinx - cosx)(sinx - cosx) = 0

4sinx = cosx
sinx/cosx = 1/4
tanx = 1/4
x = 14.0° or 194.0°

or

sinx = cosx
sinx/cosx = 1
tanx=1
x = 45° or 225°

the period of tanØ is 180°

general solutions:
45° + 180k°
14° + 180k°

notice that 45+180 = 225 , the other answer
and 14+180 = 194 , also the other answer, so we don't have to generalize those, they get hit anyway.

1. 👍 1
2. 👎 0

## Similar Questions

Solve each equation by graphing the related function. If the equation has no real-number solution, write no solution. NOTE: when I write + it has a minus on the bottom too x^2+7=0 a. x= +7 b. x = +3.5 c. x= 0 d. no solution ***

2. ### AP Calculus Help Five Questions

1. Find the particular solution to y " = 2sin(x) given the general solution y = -2sin(x) + Ax + B and the initial conditions y(pi/2) = 0 and y'(pi/2) = -2. 2. What function is a solution to the differential equation y ' - y = 0?

3. ### math;)

The equation 2sinx+sqrt(3)cotx=sinx is partially solved below. 2sinx+sqrt(3)cotx=sinx sinx(2sinx+sqrt(3)cotx)=sinx(sinx) 2sin^2x+sqrt(3)cosx=sin^2x sin^2x+sqrt(3)cosx=0 Which of the following steps could be included in the

4. ### Math

1)A piano tuner uses a tuning fork. If middle C has a frequency of 264 vibrations per second, write an equation in the form d=sinw(t) for the simple harmonic motion. 2) Verify the identity tan^2X-cot^2X/tanX+cotX=tanX-cotX I'm not

1. ### Differential Equations

Find the general solution of the given differential equation. x dy/dx − y = x^2 sin x I have solved to: y = -x cos(x) + cx The second part of the question is to give the largest interval over which the general solution is

2. ### math

sin2x-cotx = -cotxcos2x Using the various trigonometric identities(i.e. double angle formulas, power reducing formulas, half angle formulas, quotient identities, etc.) verify the identity. I first added cotx to both sides to get

3. ### Algebra

Solve the equation. Identify any extraneous solutions. √a=-2 A.4 is a solution of the original equation. B.4 is a solution of the original equation. -4 is an extraneous solution***** C.-4 is a solution of the original equation.

4. ### a math

Prove cotx-1/cotx+1 = sec2x - tan2x I prove till cotx-1/cotx+1 =1/1+tanx - tanx/1+tanx

1. ### Chemistry

If 8.5g of pure ammonium phosphate , (NH4)3PO4(s), is dissolved in distilled water to make 400mL of solution, what are the concentrations (in moles per litre) of ions in the solution. How would I solve this type of stoichiometric

2. ### calculus-differential equation

Consider the differential equation: (du/dt)=-u^2(t^3-t) a) Find the general solution to the above differential equation. (Write the answer in a form such that its numerator is 1 and its integration constant is C). u=? b) Find the

3. ### maths

find the general solution of the following first order differential equation. u(t): du/dt = u /t+2t pls show all working

4. ### math

f(x) = 4e^-1x +13x +5 at (0,9) 1. All steps for finding the first derivative of the function are clearly and accurately shown. 2. All steps for evaluating the derivative to find the slope of the tangent to the curve at the given