1A Find the rectangular coordinates of the point given in polar coordinates. (-9, – 180°) The rectangular coordinates are (Type an ordered pair.)
1A Find the rectangular coordinates of the point given in polar coordinates. (-9, – 180°) The rectangular coordinates are (Type an ordered pair.)
Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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Question
![### 1A
**Problem:**
Find the rectangular coordinates of the point given in polar coordinates.
Given Polar Coordinates:
\[
(-9, -180^\circ)
\]
**Solution:**
The rectangular coordinates are \(\boxed{\phantom{0}}\) (Type an ordered pair.)
### 1B
**Problem:**
Use a sum or difference formula to find the exact value of the trigonometric function.
Given Function:
\[
\sec\left(-\frac{\pi}{12}\right)
\]
**Solution:**
\[
\sec\left(-\frac{\pi}{12}\right) = \boxed{\phantom{0}}
\]
(Simplify your answer, including any radicals. Use integers or fractions for any numbers in the expression.)
### 1C
**Problem:**
Show that:
\[
\sin^4 \theta = \frac{3}{8} - \frac{1}{2} \cos(20\theta) + \frac{1}{8} \cos(40\theta).
\]
**Question:**
Which of the following four statements establishes the identity?
**Options:**
A.
\[
\sin^4 \theta = \left(\sin^2 2\theta \right)^2 = \left(\frac{1 - \cos(20\theta)}{2}\right)^2 = \frac{3}{8} - \frac{1}{2} \cos(20\theta) + \frac{1}{8} \cos(40\theta)
\]
B.
\[
\sin^4 \theta = \left(\sin^2 2\theta \right)^2 = \left(\frac{1 + \cos(20\theta)}{2}\right)^2 = \frac{3}{8} - \frac{1}{2} \cos(20\theta) + \frac{1}{8} \cos(40\theta)
\]
C.
\[
\sin^4 \theta = \left(\sin^2 2\theta \right)^2 = \left(\frac{1 + \cos(20\theta)}{2}\right)^2 = \frac{3}{8} - \frac{1}{2} \cos(20\theta) + \frac{1}{8} \cos(40\theta)
\]
D.
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Transcribed Image Text:### 1A
**Problem:**
Find the rectangular coordinates of the point given in polar coordinates.
Given Polar Coordinates:
\[
(-9, -180^\circ)
\]
**Solution:**
The rectangular coordinates are \(\boxed{\phantom{0}}\) (Type an ordered pair.)
### 1B
**Problem:**
Use a sum or difference formula to find the exact value of the trigonometric function.
Given Function:
\[
\sec\left(-\frac{\pi}{12}\right)
\]
**Solution:**
\[
\sec\left(-\frac{\pi}{12}\right) = \boxed{\phantom{0}}
\]
(Simplify your answer, including any radicals. Use integers or fractions for any numbers in the expression.)
### 1C
**Problem:**
Show that:
\[
\sin^4 \theta = \frac{3}{8} - \frac{1}{2} \cos(20\theta) + \frac{1}{8} \cos(40\theta).
\]
**Question:**
Which of the following four statements establishes the identity?
**Options:**
A.
\[
\sin^4 \theta = \left(\sin^2 2\theta \right)^2 = \left(\frac{1 - \cos(20\theta)}{2}\right)^2 = \frac{3}{8} - \frac{1}{2} \cos(20\theta) + \frac{1}{8} \cos(40\theta)
\]
B.
\[
\sin^4 \theta = \left(\sin^2 2\theta \right)^2 = \left(\frac{1 + \cos(20\theta)}{2}\right)^2 = \frac{3}{8} - \frac{1}{2} \cos(20\theta) + \frac{1}{8} \cos(40\theta)
\]
C.
\[
\sin^4 \theta = \left(\sin^2 2\theta \right)^2 = \left(\frac{1 + \cos(20\theta)}{2}\right)^2 = \frac{3}{8} - \frac{1}{2} \cos(20\theta) + \frac{1}{8} \cos(40\theta)
\]
D.
\
Expert Solution
Step 1
Use polar to rectangular coordinate formula
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