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Questions and Answers
What does the Greek letter theta (θ) represent in trigonometry?
What does the Greek letter theta (θ) represent in trigonometry?
What is the definition of sine (sin) in terms of the sides of a right triangle?
What is the definition of sine (sin) in terms of the sides of a right triangle?
What is the Pythagorean Identity in trigonometry?
What is the Pythagorean Identity in trigonometry?
What is the formula for the sine of the sum of two angles?
What is the formula for the sine of the sum of two angles?
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What is the Law of Cosines used for in trigonometry?
What is the Law of Cosines used for in trigonometry?
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What is the unit circle used for in trigonometry?
What is the unit circle used for in trigonometry?
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Study Notes
Theta in Trigonometry
Definition
- Theta (θ) is a Greek letter used to represent an angle in trigonometry
- It is often used as the variable in trigonometric functions such as sine, cosine, and tangent
Unit Circle
- The unit circle is a circle with a radius of 1 unit
- Theta is used to measure the angle of rotation from the positive x-axis to a point on the unit circle
- The unit circle is used to define the trigonometric functions sine, cosine, and tangent
Trigonometric Functions
- Sine (sin): sin(θ) = opposite side / hypotenuse
- Cosine (cos): cos(θ) = adjacent side / hypotenuse
- Tangent (tan): tan(θ) = opposite side / adjacent side
Identities
- Pythagorean Identity: sin^2(θ) + cos^2(θ) = 1
-
Sum and Difference Formulas:
- sin(a + b) = sin(a)cos(b) + cos(a)sin(b)
- cos(a + b) = cos(a)cos(b) - sin(a)sin(b)
- tan(a + b) = (tan(a) + tan(b)) / (1 - tan(a)tan(b))
Solving Triangles
- Theta is used to find the missing sides and angles of right triangles
- Law of Sines: a / sin(A) = b / sin(B) = c / sin(C)
- Law of Cosines: a^2 = b^2 + c^2 - 2bc cos(A)
Theta in Trigonometry
Definition of Theta
- Theta (θ) is a Greek letter representing an angle in trigonometry
- It's used as a variable in trigonometric functions like sine, cosine, and tangent
Unit Circle and Theta
- The unit circle has a radius of 1 unit
- Theta measures the angle of rotation from the positive x-axis to a point on the unit circle
- The unit circle is used to define sine, cosine, and tangent functions
Trigonometric Functions and Theta
- Sine (sin): ratio of opposite side to hypotenuse
- Cosine (cos): ratio of adjacent side to hypotenuse
- Tangent (tan): ratio of opposite side to adjacent side
Trigonometric Identities
- Pythagorean Identity: sin^2(θ) + cos^2(θ) = 1
-
Sum and Difference Formulas:
- sin(a + b) = sin(a)cos(b) + cos(a)sin(b)
- cos(a + b) = cos(a)cos(b) - sin(a)sin(b)
- tan(a + b) = (tan(a) + tan(b)) / (1 - tan(a)tan(b))
Solving Triangles with Theta
- Theta is used to find missing sides and angles in right triangles
- Law of Sines: a / sin(A) = b / sin(B) = c / sin(C)
- Law of Cosines: a^2 = b^2 + c^2 - 2bc cos(A)
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Description
Understand the concept of theta in trigonometry, its definition, and its role in the unit circle and trigonometric functions.
