Math Problem Statement

use the (x y) coordinates in the given figure to find the value of the trigonometric function at the indicated real number t sec 0

Solution

To evaluate the trigonometric function sec(0)\sec(0) using the (x,y)(x, y) coordinates on the unit circle, we need to recall the relationship between the secant function and the cosine function. The secant function is defined as the reciprocal of the cosine function:

sec(θ)=1cos(θ)\sec(\theta) = \frac{1}{\cos(\theta)}

For the angle 00 radians, the point on the unit circle is (1,0)(1, 0). The cosine function corresponds to the xx-coordinate of the point on the unit circle, so:

cos(0)=1\cos(0) = 1

Now, using the definition of secant:

sec(0)=1cos(0)=11=1\sec(0) = \frac{1}{\cos(0)} = \frac{1}{1} = 1

Therefore, the value of sec(0)\sec(0) is 11.

Would you like to explore further details or explanations?

Here are 5 related questions to deepen your understanding:

  1. What is the value of sec(π/2)\sec(\pi/2)?
  2. How does the secant function behave for angles in different quadrants?
  3. What are the reciprocal trigonometric functions of sine and tangent?
  4. How is sec(θ)\sec(\theta) related to the unit circle?
  5. What is the domain and range of the secant function?

Tip: Always remember that secant is undefined where the cosine function equals zero.

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Math Problem Analysis

Mathematical Concepts

Trigonometry
Unit Circle
Secant Function
Reciprocal Trigonometric Functions

Formulas

sec(θ) = 1 / cos(θ)
cos(θ) is the x-coordinate on the unit circle

Theorems

Unit Circle Theorem
Reciprocal Trigonometric Functions

Suitable Grade Level

Grades 9-11