Evaluate Trig Expressions....Part 1

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In summary, to evaluate trigonometric expressions using the method shown in the textbook, follow these steps: 1. Determine the quadrant in which the angle falls. 2. Find the reference angle by subtracting the angle from a multiple of 360 degrees. 3. Evaluate the trig function of the reference angle. For angles that are negative, find the coterminal angle by adding or subtracting multiples of 360 degrees until the angle falls within the range of 0 to 360 degrees. The reference angle for an angle in Quadrant III is the difference between the angle and 360 degrees. The reference angle for an angle in Quadrant II is the difference between 180 degrees and the angle. The reference angle for
  • #1
mathdad
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Evaluate the trig expressions using the method shown in the textbook. Steps A through C show the method given in the textbook.

1. sin 210°

A. We are told to graph sin 210°. We are in Quadrant 3.

B. Find the reference angle R.

R = 270° - 210°

R = 60°

C. Evaluate sin R.

sin 60° = -sqrt{3}/2

Book's answer is -1/2.

2. sin (-210°)

A. We are told to graph sin (-210°).
We are in Quadrant 2.

B. Find the reference angle R.

R = -270° - (-210°)

R = -270° + 210°

R = -60

C. Evaluate sin R

sin (-60°) = sqrt{3}/2

Book's answer is 1/2.
 
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  • #2
1. reference angle for 210 is 30 degrees, not 60. sin(30) = 1/2, but since the reference angle is in quad III where sine is negative, sin(210) = -1/2

2. -210 is coterminal with 150

reference angle is 30 in quad II where sine is positive

sin(30) = 1/2
 
  • #3
skeeter said:
1. reference angle for 210 is 30 degrees, not 60. sin(30) = 1/2, but since the reference angle is in quad III where sine is negative, sin(210) = -1/2

2. -210 is coterminal with 150

reference angle is 30 in quad II where sine is positive

sin(30) = 1/2

Is there a formula(s) for finding the reference angle and coterminal angle in trigonometry?
 

FAQ: Evaluate Trig Expressions....Part 1

What is the purpose of evaluating trig expressions?

The purpose of evaluating trig expressions is to simplify and find the numerical value of the expression using trigonometric identities and rules.

What are the key components of a trig expression?

The key components of a trig expression are trigonometric functions (such as sine, cosine, tangent), variables (such as x or theta), and constants (such as pi or e).

What are the steps to evaluating a trig expression?

The steps to evaluating a trig expression are: 1) Simplify the expression using trigonometric identities and rules, 2) Substitute any given values for the variables, 3) Evaluate the resulting expression using a calculator or by hand if possible.

What are some common errors to avoid when evaluating trig expressions?

Some common errors to avoid when evaluating trig expressions include: 1) Forgetting to use parentheses when simplifying, 2) Misinterpreting the order of operations, 3) Forgetting to convert from degrees to radians or vice versa, and 4) Making mistakes when using a calculator.

How can evaluating trig expressions be useful in real life?

Evaluating trig expressions can be useful in real life in a variety of fields, such as engineering, architecture, and physics. It can be used to solve problems involving angles and distances, as well as in the construction and design of structures and devices.

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