Trigonometric Functions And Identities

In summary, the conversation is about a person struggling to solve for x in a trigonometric equation and trying different methods such as using the identity tan^2(x) + 1 = sec^2(x) and converting everything in terms of cos (x). The conversation also mentions using factoring, completing the square, and the quadratic formula as methods for solving quadratic equations.
  • #1
wanchosen
19
0
Hi there,

I am struggling to solve for x in the following problem:-

Find all values of x in the interval 0<= x <= 360 for which: tan^2(x) = 5sec(x) - 2

I have used the identity tan^2(x) + 1 = sec^2(x) to get:

sec^2(x) - 1 = 5sec(x) - 2

and rearranged to get

sec^2(x) - 5sec(x) + 1 = 0

but I can't factor this or solve for x. Can anyone help please?
 
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  • #2
wanchosen said:
Can anyone help please?
Why did you spend all of that effort to turn it into a quadratic equation?
 
  • #3
I assumed that I need to get all the trig functions of the same type before I can solve for x. Using the identity for sec^2(x) seemed the obvious choice...which lead me to a quadratic. I couldn't see how else to solve for x. I also tried converting everything in terms of cos (x) which was more messy. I may be mistaken, but from previous questions I have answered like this, tend to lead to a quadratic to factor for a solution/s for x.
 
  • #4
wanchosen said:
tend to lead to a quadratic to factor for a solution/s for x.
Is factoring the only method you know for solving quadratic equations, or do you know other methods?
 
  • #5
Completing the square, or using the quadratic formula are another two methods.
 
  • #6
Thanks, tried completing the square to solve the quadratic and this worked.
 

1. What are the primary trigonometric functions?

The primary trigonometric functions are sine, cosine, and tangent. These functions represent the ratios of the sides of a right triangle and are used to solve problems involving triangles and circular motion.

2. What are the reciprocal trigonometric functions?

The reciprocal trigonometric functions are cosecant, secant, and cotangent. These functions are the reciprocals of the primary trigonometric functions and are used to solve problems involving triangles and circular motion.

3. What are the Pythagorean identities?

The Pythagorean identities are mathematical equations that express relationships between the primary trigonometric functions and their squares. They are used to simplify trigonometric expressions and solve trigonometric equations.

4. How are trigonometric functions used in real life?

Trigonometric functions are used in various fields such as engineering, physics, and astronomy to model and solve problems involving angles and distances. They are also used in navigation, architecture, and music.

5. How can I prove trigonometric identities?

To prove a trigonometric identity, you can use algebraic manipulation, properties of trigonometric functions, and trigonometric identities. You can also use the unit circle and graphing techniques to verify identities. Practice and familiarity with trigonometric functions are essential for proving identities.

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