A student is given four different trigonometric expressions 1 I secx cosx 9 II cot²x-csc² x III 2cos²x+2sin²x 2 cos x IV 2 cotx- sin x If the expression are simplified are ranked, from smallest to largest, what is the correct order? Show all the steps and state the name of appropriate formula you used in each step. For example: III: 2cos²x + 2sin²x = 2(cos²x+sin²x) = 2 (1) This step uses Pythagorean identity. = 2 The names of formula you might required are: Cofunction formula / compound angle formula (for sine, cosine, tangent) / double angle formula (for sine, cosine, tangent) / reciprocal identities / quotient identities / Pythagorean identities / etc.

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...
Question
A student is given four different trigonometric expressions
1
I
-secx cosx
II
cot²x-csc² x
III
2cos²x+2sin²x
2 cos x
IV
2cotx--
sinx
If the expression are simplified are ranked, from smallest to largest, what is the correct order?
Show all the steps and state the name of appropriate formula you used in each step.
For example:
III: 2cos²x + 2sin²x
= 2(cos²x+ sin²x)
= 2 (1)
This step uses Pythagorean identity.
= 2
The names of formula you might required are:
Cofunction formula / compound angle formula (for sine, cosine, tangent) / double angle formula
(for sine, cosine, tangent) / reciprocal identities / quotient identities / Pythagorean identities / etc.
Transcribed Image Text:A student is given four different trigonometric expressions 1 I -secx cosx II cot²x-csc² x III 2cos²x+2sin²x 2 cos x IV 2cotx-- sinx If the expression are simplified are ranked, from smallest to largest, what is the correct order? Show all the steps and state the name of appropriate formula you used in each step. For example: III: 2cos²x + 2sin²x = 2(cos²x+ sin²x) = 2 (1) This step uses Pythagorean identity. = 2 The names of formula you might required are: Cofunction formula / compound angle formula (for sine, cosine, tangent) / double angle formula (for sine, cosine, tangent) / reciprocal identities / quotient identities / Pythagorean identities / etc.
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