Podcast
Questions and Answers
The ______ identity states that csc x = 1 / sin x.
The ______ identity states that csc x = 1 / sin x.
reciprocal
The ______ identity states that tan x = sin x / cos x.
The ______ identity states that tan x = sin x / cos x.
quotient
To solve for sin x in this case, we must use the ______ ______ identity.
To solve for sin x in this case, we must use the ______ ______ identity.
Pythagorean Theorem
The ______ identity states that cos (-x) = cos x.
The ______ identity states that cos (-x) = cos x.
The ______ identity states that cos (-π/2 + θ) = sin θ.
The ______ identity states that cos (-π/2 + θ) = sin θ.
When simplifying the expression, we can substitute sec x with 1 / ______.
When simplifying the expression, we can substitute sec x with 1 / ______.
We can then simplify the expression using the ______ identity.
We can then simplify the expression using the ______ identity.
To prove a trigonometric identity, we must begin with one side of the equation and manipulate it to match the ______ side.
To prove a trigonometric identity, we must begin with one side of the equation and manipulate it to match the ______ side.
What is the value of csc x if sin x = 2√5 / 5?
What is the value of csc x if sin x = 2√5 / 5?
What is the value of cos a if tan a = √2 / 2 and sin a = -√3 / 2?
What is the value of cos a if tan a = √2 / 2 and sin a = -√3 / 2?
What is the value of sin x if cot x = -√3 / 2 and cos x < 0?
What is the value of sin x if cot x = -√3 / 2 and cos x < 0?
What is the value of cot θ if cos θ = -7 / 12 and sin θ < 0?
What is the value of cot θ if cos θ = -7 / 12 and sin θ < 0?
What is the value of tan (-x) if cot (-x) = -1.84?
What is the value of tan (-x) if cot (-x) = -1.84?
What is the value of cos (-π/2 + θ) if sin θ = -0.57?
What is the value of cos (-π/2 + θ) if sin θ = -0.57?
Which of the following is a simplified form of sec x * sin² x + cos x?
Which of the following is a simplified form of sec x * sin² x + cos x?
Which of the following is a simplified form of csc ß - sin ß / sin ß?
Which of the following is a simplified form of csc ß - sin ß / sin ß?
Flashcards
Cosecant Definition
Cosecant Definition
Csc x is the reciprocal of sin x.
Finding cosine from tangent
Finding cosine from tangent
Cos a can be found using sin a and tan a.
Pythagorean Identity
Pythagorean Identity
sin² x + cos² x = 1 applies to trigonometric functions.
Cotangent Definition
Cotangent Definition
Cot θ is the ratio of cos θ to sin θ.
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Even-Odd Identities
Even-Odd Identities
Tan(-x) = -tan(x) due to odd behavior.
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Cofunction Identity
Cofunction Identity
cos(-π/2 + θ) = sin θ.
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Secant Simplification
Secant Simplification
Sec x = sin² x/cos x + cos x simplifies to 1/cos x.
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Cosecant Derivation
Cosecant Derivation
csc ß - sin ß/sin ß simplifies to cos² ß/sin ß.
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Csc x from sin x
Csc x from sin x
If sin x = 2√5 / 5, then csc x = √5 / 2.
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Finding cos a from tan and sin
Finding cos a from tan and sin
Cos a can be calculated as cos a = (-√3 / 2) / (√2 / 2).
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Cotangent and sine relationship
Cotangent and sine relationship
Cot x = cos x / sin x relates cotangent to sine and cosine.
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Find sin x using cot x
Find sin x using cot x
Using cot x = -√3 / 2, find sin x = 2√7 / 7.
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Cotangent value from cosine
Cotangent value from cosine
Cot θ = -7 / √95 when cos θ = -7 / 12 and sin θ < 0.
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Tan of negative angle
Tan of negative angle
Tan (-x) can be calculated as tan (-x) = -1 / 1.84.
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Cofunction identity with sine
Cofunction identity with sine
cos(-π/2 + θ) = sin θ relates cos of a combination angle to sine.
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Simplifying sin with cotangent
Simplifying sin with cotangent
sin y + sin y * cot² y / csc y simplifies to csc y.
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Trigonometric Identities and Equations
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Reciprocal and Quotient Identities: Used for questions 1 & 2
- csc x = 1/sin x
- sec x = 1/cos x
- tan x = sin x/cos x
- cot x = cos x/sin x
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Pythagorean Theorem Identities: Used for questions 3 & 4
- sin² x + cos² x = 1
- 1 + tan² x = sec² x
- 1 + cot² x = csc² x
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Cofunction and Even-Odd Identities: Used for questions 5 & 6
- These identities relate trigonometric functions of complementary angles and functions of negative angles.
- Examples are needed to detail the cofunction and even-odd identities
- Specific examples (e.g., sin(90° - θ) = cos θ, cos(-x) = cos x, etc.) are needed to provide specific formulas.
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Simplifying Trigonometric Expressions (Questions 7-10):
- Involves manipulating trigonometric expressions using identities to simplify. Example: Simplifying sec x sin² x + cos x / cos x
- Example problem 8, simplifying csc β - sin β / sin β.
- An example of a simplified expression: cos²β / sinβ.
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Proving Trigonometric Identities (Questions 11-12): - Involve showing that one trigonometric expression is equal to another using established identities. - Example problem 12, proving that sin a / (1 - cos a) = csc a + cot a - Additional examples of identities are needed to clarify this section.
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Description
Test your knowledge on trigonometric identities and equations through a variety of questions. This quiz covers reciprocal, quotient, Pythagorean, cofunction, and even-odd identities, as well as simplifying expressions and proving identities. Master these essential concepts to excel in trigonometry.