Where trigonometric identities come from

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Mathematics
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11th Grade - University
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Hard
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10 questions
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1.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
What is the primary purpose of introducing the unit circle in trigonometry?
To memorize trigonometric tables
To understand calculus concepts
To solve algebraic equations
To evaluate trigonometric functions easily
2.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
Which of the following is a reciprocal identity?
sin(θ) = 1/csc(θ)
tan(θ) = sin(θ)/cos(θ)
cos(θ) = 1/sec(θ)
cot(θ) = cos(θ)/sin(θ)
3.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
What is the quotient identity for tangent?
tan(θ) = 1/cot(θ)
tan(θ) = cos(θ)/sin(θ)
tan(θ) = sin(θ)/cos(θ)
tan(θ) = 1/sec(θ)
4.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
What is the Pythagorean identity involving sine and cosine?
tan²(θ) + 1 = sec²(θ)
sin²(θ) + cos²(θ) = 1
sin(θ) + cos(θ) = 1
1 + cot²(θ) = csc²(θ)
5.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
Which of the following is a Pythagorean identity?
sin(θ) = 1/csc(θ)
cos(θ) = 1/sec(θ)
tan(θ) = sin(θ)/cos(θ)
1 + tan²(θ) = sec²(θ)
6.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
Which trigonometric function is even?
csc(θ)
cos(θ)
tan(θ)
sin(θ)
7.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
Which identity is derived from the symmetry of the sine function?
tan(-θ) = -tan(θ)
csc(-θ) = -csc(θ)
cos(-θ) = cos(θ)
sin(-θ) = -sin(θ)
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