# Evaluate Trig Expressions....Part 2

• MHB
In summary, to evaluate the trig expressions cos 4π/3 and sec 4π/3 using the method shown in the textbook, we first find the reference number r by subtracting the given angle from 3π/2. Then, we evaluate the reference angle π/6 and use it to find the cosine and secant values, which are -√3/2 and -2√3/3 respectively. The textbook's answers for r are -1/2 and -2, respectively. It is recommended to practice finding reference angles using the algebraic method over graphing for better understanding.
Evaluate the trig expressions using the method shown in the textbook. Steps A through C show the method given in the textbook.

1. cos 4π/3

A. We are told to graph cos 4π/3. We are in Quadrant 3.

B. Find the reference number r.

r = 3π/2 - 4π/3

r = π/6

C. Evaluate r.

cos π/6 = -sqrt{3}/2

Book's answer for r is -1/2.

2. sec 4π/3

A. We are told to graph sec 4π/3.

B. Find the reference number r.

r = 3π/2 - 4π/3

r = π/6

C. Evaluate r.

sec π/6 = -2sqrt{3}/3.

Book's answer for r is -2.

$\dfrac{4\pi}{3}$ is in quad III $\implies$ cosine is negative

reference angle is $\dfrac{4\pi}{3} - \pi = \dfrac{\pi}{3} \implies \cos\left(\dfrac{4\pi}{3}\right) = -\cos\left(\dfrac{\pi}{3}\right) = - \dfrac{1}{2}$

I will practice more on finding reference angles using the algebraic method you provided in Part 1, I believe. It's a very easy concept but using the graph can be a bit tricky. I prefer using algebra over graphing any time.

## 1. What is the purpose of evaluating trig expressions?

Evaluating trig expressions is used to simplify and find the exact numerical value of a trigonometric equation or expression. This can be helpful in solving real-world problems or verifying the accuracy of a given trigonometric identity.

## 2. How do I evaluate a trig expression?

To evaluate a trig expression, you must first understand the basic trigonometric functions (sine, cosine, tangent, etc.) and their corresponding unit circle values. Then, you can use algebraic techniques such as factoring, simplifying, and substituting values to simplify the expression and find its numerical value.

## 3. Can I use a calculator to evaluate trig expressions?

Yes, you can use a scientific calculator to evaluate trig expressions. Most calculators have special buttons for trigonometric functions and inverse trigonometric functions, making it easier to input and evaluate these types of expressions.

## 4. Are there any common mistakes to avoid when evaluating trig expressions?

One common mistake when evaluating trig expressions is forgetting to convert angles from degrees to radians or vice versa. It's important to use the correct unit of measure when working with trigonometric functions. Another mistake is not simplifying the expression enough, which can lead to incorrect answers.

## 5. How can I check if my evaluated trig expression is correct?

You can check if your evaluated trig expression is correct by plugging in the numerical value of the angle into the original expression and simplifying. If the two expressions are equal, then your evaluation is correct. You can also use a calculator to verify the numerical value of the expression.

• General Math
Replies
2
Views
1K
• General Math
Replies
3
Views
1K
• General Math
Replies
4
Views
2K
• General Math
Replies
2
Views
954
• General Math
Replies
11
Views
3K
• General Math
Replies
6
Views
2K
• Calculus and Beyond Homework Help
Replies
3
Views
1K
• General Math
Replies
8
Views
1K
• Precalculus Mathematics Homework Help
Replies
5
Views
2K
• General Math
Replies
4
Views
2K