# Trig #3 (Part solutions included)

• lovemake1
In summary: No, this is not correct. You're forgetting that you're supposed to solve an inequality, not an equation.
lovemake1

## Homework Statement

sec^2x - 3secx + 2 < 0

## The Attempt at a Solution

sec^2x - 3secx + 2 < 0

ok so this can be written as, (secx - 2)(secx -1) < 0
this means secx is between 1 and 2 right ?

secx = 2 and secx = 1

would we find all the solutions that's between 1 and 2 ?
please check if my understanding is correct.

Sounds good.

lovemake1 said:

## Homework Statement

sec^2x - 3secx + 2 < 0

## The Attempt at a Solution

sec^2x - 3secx + 2 < 0

ok so this can be written as, (secx - 2)(secx -1) < 0
this means secx is between 1 and 2 right ?

secx = 2 and secx = 1

would we find all the solutions that's between 1 and 2 ?
please check if my understanding is correct.
ab< 0 as long as a and b have different signs. Since 2> 1, secx- 2< secx- 1 so you want sec x- 2< 0 and sec x- 1> 0. That is, as you say, 1< sec x< 2.

secx= 1 is the same as 1/cosx= 1 or cos x= 1. sec x= 2 is the same as cos(x)= 1/2. and note that 1< 1/cos(x)< 2 is the same as cos(x)< 1< 2cos(x) or 1/2< cos(x)< 1.
Of course, if you are asked for all such x, not just between 0 and $\pi/2$ or 0 and $2\pi$, there will be many intervals in which that is true.

so the two solutions are, cosx = 1 and cosx = 1/2

since x belongs to [0,2pi), x = 0, 1/3pi
Could someone correct me if I am wrong, i think i got the right answer.

lovemake1 said:
so the two solutions are, cosx = 1 and cosx = 1/2

since x belongs to [0,2pi), x = 0, 1/3pi
Could someone correct me if I am wrong, i think i got the right answer.
No, this is not correct. You're forgetting that you're supposed to solve an inequality, not an equation. Reread HallsofIvy's post.

oh right, here are my fixed answer.

x belongs to (1pi/3, 1pi/3)

are they correct?
i didnt include 0, because x must be < cos = 1

Last edited:

## 1. What is the definition of a trigonometric function?

A trigonometric function is a mathematical function that relates the angles of a triangle to the lengths of its sides. The most commonly used trigonometric functions are sine, cosine, and tangent.

## 2. How do you solve trigonometric equations?

To solve a trigonometric equation, you must isolate the variable on one side of the equation and use trigonometric identities and properties to simplify the equation. Then, use inverse trigonometric functions to find the value of the angle that satisfies the equation.

## 3. What are the key properties of trigonometric functions?

The key properties of trigonometric functions include periodicity, even and odd symmetry, and amplitude and phase shift. These properties allow for the transformation and manipulation of trigonometric functions to solve equations and graph functions.

## 4. How do you use the unit circle to solve trigonometric problems?

The unit circle is a circle with a radius of 1, used in trigonometry to easily determine the values of trigonometric functions at any angle. By using the coordinates of points on the unit circle, you can find the values of sine, cosine, and tangent for any angle, allowing you to solve various trigonometric problems.

## 5. What is the practical application of trigonometry?

Trigonometry has many practical applications in fields such as engineering, physics, and navigation. It is used to calculate distances, angles, and heights in real-world situations, such as building construction, satellite navigation, and surveying land.

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