68.4k views
0 votes
6 cos x - 5 sin x = 0
solve in the interval 0

User Ptica
by
8.2k points

1 Answer

4 votes

Final answer:

To solve the equation '6 cos x - 5 sin x = 0', first express it in terms of one trigonometric function '6 = 5 tan x' and then find x such that 'tan x = 6/5' within the interval 0 < x < 2π.

Step-by-step explanation:

To solve the trigonometric equation 6 cos x - 5 sin x = 0, we start by isolating one of the trigonometric functions:
6 cos x = 5 sin x
Divide both sides by cos x (assuming cos x is not zero):
6 = 5 tan x
Now divide by 5:
tan x = ±6/5

Find the angle whose tangent is 6/5. This can be done using a calculator or trigonometric tables.

The solutions in the interval 0 < x < 2π would be the angles where the tangent has the value of 6/5, as well as the angles in the third or fourth quadrant where the tangent also equals 6/5.

Remember that tan x is positive in the first and third quadrants, so you must check for solutions in those quadrants.

User Mark Olsen
by
7.6k points

No related questions found

Welcome to QAmmunity.org, where you can ask questions and receive answers from other members of our community.