How Do You Solve sqrt(3) sec x = -2 for x in Radians?

In summary, the solution to the equation sqrt(3) sec x = -2 is x = 5π/6 + 2πn or x = 7π/6 + 2πn, where n is any integer.
  • #1
hailey51
4
0
Find Exact Radian Solution OR to nearest 100th of a radian

sqrt(3) sec x = -2
 
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  • #2
You need to at least show an attempt here before anyone can help you. Look at a graph of sec(x).
 
  • #3
Dick said:
You need to at least show an attempt here before anyone can help you. Look at a graph of sec(x).

well, would the first step be changing it to
cos x = - (sqrt 3)/2

?
 
  • #4
hailey51 said:
well, would the first step be changing it to
cos x = - (sqrt 3)/2

?

Yes.

For what angles is cosine = -(√3)/2 ?
 
  • #5
SammyS said:
Yes.

For what angles is cosine = -(√3)/2 ?

This is where I get confused...
it's not ∏/6 right? because it's negative
so it could be the 5∏/6 ?
and is that the only answer?
 
  • #6
Since sine and cosine are periodic with period [itex]2\pi[/itex], no that is not the only solution.
 
  • #7
HallsofIvy said:
Since sine and cosine are periodic with period [itex]2\pi[/itex], no that is not the only solution.

Oh, would the other solution be 7π/6 +2πn ?
 
  • #8
hailey51 said:
Oh, would the other solution be 7π/6 +2πn ?

Right.
 

FAQ: How Do You Solve sqrt(3) sec x = -2 for x in Radians?

How do I solve a trigonometry equation?

To solve a trigonometry equation, you will need to use the trigonometric identities and properties, such as the Pythagorean theorem and the unit circle. You will also need to use algebraic techniques, such as factoring and substitution. It is important to carefully follow the steps and make sure to keep track of any restrictions on the domain of the equation.

What are the common trigonometric identities used to solve equations?

Some of the common trigonometric identities used to solve equations include the Pythagorean identities (sin^2x + cos^2x = 1), the double angle identities (sin2x = 2sinx cosx), and the sum and difference identities (sin(x+y) = sinx cosy + cosx siny). It is important to be familiar with these identities to solve trigonometry equations efficiently.

How do I determine the solution set for a trigonometry equation?

To determine the solution set for a trigonometry equation, you will need to use the inverse trigonometric functions, such as arcsin, arccos, and arctan. These functions will help you find the angles that satisfy the equation. It is important to remember that trigonometric equations may have multiple solutions, so be sure to check all possibilities.

Can I use a calculator to solve trigonometry equations?

Yes, you can use a calculator to solve trigonometry equations. Most scientific calculators have the necessary trigonometric functions and inverse trigonometric functions needed to solve equations. However, it is important to understand the concepts and steps involved in solving equations by hand before relying on a calculator.

Are there any tips for solving trigonometry equations?

Some tips for solving trigonometry equations include practicing with different types of equations, thoroughly understanding the trigonometric identities, and carefully tracking the restrictions on the domain. It is also helpful to check your answer by plugging it back into the original equation and simplifying both sides.

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