Understanding Trig Function Questions in the Range of Pi to 2Pi

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In summary, the conversation is about determining the larger angle in the range of pi to 2pi, given that secant is equal to 1.2048. The solution involves using the inverse cosine function and converting the angle to radians.
  • #1
DethRose
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Im having some problems with some trig function question...im not really understanding what they are asking with these type of questions?

help please

determine the larger angle a in the range pie<a<2pie

sec A = 1.2048

answer a= (in radians)

the answer is 5.6915 rads
 
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  • #2
ok so the question is that we want to determine the larger angle [tex] \alpha [/tex] in the range [tex] \pi < \alpha < 2\pi [/tex]

Now [tex] \sec x = \frac{1}{\cos x} [/tex] See if you can go from here.
 
  • #3
First, start off by writing secant as a cosine function:

[tex]\frac{1}{\cos A}=1.2048[/tex]

Now, solve the function for A. Remember, [itex]\arccos A[/itex] is only defined from 0 to [itex]\pi[/itex] so you have to find a corresponding angle between [itex]\pi[/itex] and [itex]2\pi[/itex]

good luck.
 
  • #4
yea but how do i put it in radians?
 
  • #5
This question would make more sense if asked about the range from 0 to [itex]2\pi[/itex], since there would be two angles with sec = 1.2048. But there's only one in the range of [itex]\pi[/itex] to [itex]2\pi[/itex], so the question doesn't make that much sense.
 

1. What are the six trigonometric functions?

The six trigonometric functions are sine, cosine, tangent, cotangent, secant, and cosecant. These functions represent the ratios of the sides of a right triangle in relation to its angles.

2. How do you solve trigonometric function problems?

To solve a trigonometric function problem, you can use the basic trigonometric identities and formulas, such as the Pythagorean identities and the double angle formulas. You can also use the unit circle to find the values of the trigonometric functions for specific angles.

3. What is the unit circle and how is it used in trigonometry?

The unit circle is a circle with a radius of one unit, centered at the origin on a coordinate plane. It is used in trigonometry to find the values of the trigonometric functions for specific angles. The x-coordinate of a point on the unit circle represents the cosine of the angle, while the y-coordinate represents the sine. The unit circle is also used to define the other trigonometric functions, such as tangent, cotangent, secant, and cosecant.

4. What are the common applications of trigonometric functions?

Trigonometric functions are used in various fields, such as engineering, physics, and navigation. They are used to solve problems involving angles and distances, such as finding the height of a building or the distance between two points. Trigonometric functions are also used in modeling periodic phenomena, such as sound waves and electrical currents.

5. How do you use trigonometric functions to solve real-life problems?

To solve real-life problems using trigonometric functions, you need to understand the problem and identify the relevant angles and sides. Then, you can use the trigonometric functions and formulas to set up and solve equations. It is important to carefully label the sides and angles in the problem to accurately apply the trigonometric functions.

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