i need help answering this trig problem?

Question

the problem is

2cosx+sinx=0

if you could please show me the steps and answers. i need the answer between 0 and 360 degrees

Solve the following equation for all solutions between 0 and 360 degrees and 0 and 2pi.

2cosx+sinx=0


if you could please show me the steps and answers please i would greatly apprechiate it

Answer 1

Hi,

They're at 116.57° and 296.565°.

Just enter into your graphing calculator: Y1 = 2cos(x) + sin(x) and look for x intercepts when xmin=0, xmax=360, xscl=90, ymin = -3, ymax = 3, yscl = 1. The values above are the answers!!

I hope that helps!! :-)

Answer 2

First, if cos x = 0, sin x <> 0, so we can divide by
cos x:
sin x/cos x = -2
That gives
tan x = -2.
Thus x is an angle in the second or fourth quadrant.
The base solution is x = arctan(2) = 63.43 deg.
So the 2 solutions of the equation are 116.565 deg.
and 296.565 deg.

Answer 3

subtract sinx to get:
2cosx = -sinx

divide by cosx to get:
2 = -sinx/cosx

since sinx/cosx = tanx:
2 = -tanx or tanx = -2

now use your calculator to evaluate.
you will have answers in the 2nd and 4th quadrants because tangent is negative there. It is positive in the 1st and the 3rd.

when using your calculator, make certain that your mode is in degrees, not radians, for this problem.

now, type in tan^-1(-2) by pressing 2nd and then tan to get:
-63.435

63.435 is the reference angle.

so, 180-63.435 will get the asnswer in the 2nd quadrant, which is 116.565 degrees and 180-63.435 will get the answer in the 4th quadrant, which is 296.565 degrees.

116.565 and 296.565 degrees are the answers.

Answer 4

Sine is defined by utilizing opposite divide by utilizing hypoteneuse, meaning that 24 is the alternative area to attitude theta, and 25 is the hypoteneuse. The final area, the adjoining area to attitude theta, may be got here across with the aid of Pythagoreans' Theorem: 25^2 = 24^2 + x^2 -> x^2 = 625 - 576 = 40 9 -> x = 7. this implies that cos(theta) = 7/25 on the grounds that cosine is adjoining divided by utilizing the hypoteneuse, tan(theta) = 24/7, because it extremely is sin(theta) /cos(theta); it is likewise opposite divided by utilizing adjoining. sec(theta) = 25/7, on the grounds that secant is defined by utilizing one million divided by utilizing cosine, and is likewise hypoteneuse divided by utilizing adjoining. In precis: cos(theta) = 7/25 tan(theta) = 24/7 sec(theta) = 25/7