Use the given function values and the trigonometric identities to find the exact value of each indicated trigonometric function. √3 sin(60°) = , cos(60°) = 1/2 2 (a) sin(30°) (b) cos(30°) (c) tan (60°) (d) cot(60°)
Use the given function values and the trigonometric identities to find the exact value of each indicated trigonometric function. √3 sin(60°) = , cos(60°) = 1/2 2 (a) sin(30°) (b) cos(30°) (c) tan (60°) (d) cot(60°)
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter6: The Trigonometric Functions
Section: Chapter Questions
Problem 4DE
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![## Finding Exact Values of Trigonometric Functions
### Instructions
Use the given function values and the trigonometric identities to determine the exact value of each indicated trigonometric function.
### Given Values
\[ \sin(60^\circ) = \frac{\sqrt{3}}{2} \]
\[ \cos(60^\circ) = \frac{1}{2} \]
### Questions
(a) Determine \( \sin(30^\circ) \):
\[ \sin(30^\circ) = \]
\[ \boxed{\quad\quad} \]
(b) Determine \( \cos(30^\circ) \):
\[ \cos(30^\circ) = \]
\[ \boxed{\quad\quad} \]
(c) Determine \( \tan(60^\circ) \):
\[ \tan(60^\circ) = \]
\[ \boxed{\quad\quad} \]
(d) Determine \( \cot(60^\circ) \):
\[ \cot(60^\circ) = \]
\[ \boxed{\quad\quad} \]
### Explanation
To find these values, you can use known trigonometric identities and the exact values of trigonometric functions for common angles. For example:
- Use the identity \( \sin(90^\circ - \theta) = \cos(\theta) \) and \( \cos(90^\circ - \theta) = \sin(\theta) \) to find \( \sin(30^\circ) \) and \( \cos(30^\circ) \).
- Use the definition \( \tan(\theta) = \frac{\sin(\theta)}{\cos(\theta)} \) to find \( \tan(60^\circ) \).
- Use the definition \( \cot(\theta) = \frac{1}{\tan(\theta)} \) to find \( \cot(60^\circ) \).](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fa0e38307-1ade-44bc-b712-aaeda4c58098%2F78456083-2254-4780-92aa-982346875f7d%2Frm1y7w_processed.png&w=3840&q=75)
Transcribed Image Text:## Finding Exact Values of Trigonometric Functions
### Instructions
Use the given function values and the trigonometric identities to determine the exact value of each indicated trigonometric function.
### Given Values
\[ \sin(60^\circ) = \frac{\sqrt{3}}{2} \]
\[ \cos(60^\circ) = \frac{1}{2} \]
### Questions
(a) Determine \( \sin(30^\circ) \):
\[ \sin(30^\circ) = \]
\[ \boxed{\quad\quad} \]
(b) Determine \( \cos(30^\circ) \):
\[ \cos(30^\circ) = \]
\[ \boxed{\quad\quad} \]
(c) Determine \( \tan(60^\circ) \):
\[ \tan(60^\circ) = \]
\[ \boxed{\quad\quad} \]
(d) Determine \( \cot(60^\circ) \):
\[ \cot(60^\circ) = \]
\[ \boxed{\quad\quad} \]
### Explanation
To find these values, you can use known trigonometric identities and the exact values of trigonometric functions for common angles. For example:
- Use the identity \( \sin(90^\circ - \theta) = \cos(\theta) \) and \( \cos(90^\circ - \theta) = \sin(\theta) \) to find \( \sin(30^\circ) \) and \( \cos(30^\circ) \).
- Use the definition \( \tan(\theta) = \frac{\sin(\theta)}{\cos(\theta)} \) to find \( \tan(60^\circ) \).
- Use the definition \( \cot(\theta) = \frac{1}{\tan(\theta)} \) to find \( \cot(60^\circ) \).
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