Podcast
Questions and Answers
What is the ratio of the opposite side to the adjacent side in a right-angled triangle?
What is the ratio of the opposite side to the adjacent side in a right-angled triangle?
What is the angle between the line of sight and the horizontal when looking down at an object?
What is the angle between the line of sight and the horizontal when looking down at an object?
What is the equation that is true for all values of the variables, such as sin(A) = cos(90° - A)?
What is the equation that is true for all values of the variables, such as sin(A) = cos(90° - A)?
What is the ratio of the adjacent side to the hypotenuse in a right-angled triangle?
What is the ratio of the adjacent side to the hypotenuse in a right-angled triangle?
Signup and view all the answers
What is the equation that relates the sides of a right-angled triangle, such as a^2 = b^2 + c^2 - 2bc * cos(A)?
What is the equation that relates the sides of a right-angled triangle, such as a^2 = b^2 + c^2 - 2bc * cos(A)?
Signup and view all the answers
What is the acute angle between the terminal side of an angle and the x-axis?
What is the acute angle between the terminal side of an angle and the x-axis?
Signup and view all the answers
What is the equation that is true for all right-angled triangles, such as sin^2(A) + cos^2(A) = 1?
What is the equation that is true for all right-angled triangles, such as sin^2(A) + cos^2(A) = 1?
Signup and view all the answers
Study Notes
Trigonometry
Sine, Cosine, and Tangent
-
Sine (sin): Ratio of the opposite side to the hypotenuse in a right-angled triangle.
- sin(A) = opposite side / hypotenuse
-
Cosine (cos): Ratio of the adjacent side to the hypotenuse in a right-angled triangle.
- cos(A) = adjacent side / hypotenuse
-
Tangent (tan): Ratio of the opposite side to the adjacent side in a right-angled triangle.
- tan(A) = opposite side / adjacent side
Angles and Triangles
- Right-angled triangle: A triangle with one right angle (90°).
- Angle of elevation: The angle between the line of sight and the horizontal when looking up at an object.
- Angle of depression: The angle between the line of sight and the horizontal when looking down at an object.
- Reference angle: The acute angle between the terminal side of an angle and the x-axis.
Solving Triangles
- Pythagorean identity: sin^2(A) + cos^2(A) = 1
- Sine rule: a / sin(A) = b / sin(B) = c / sin(C) (for any triangle with sides a, b, c and angles A, B, C)
- Cosine rule: a^2 = b^2 + c^2 - 2bc * cos(A) (for any triangle with sides a, b, c and angle A)
- Trigonometric identities: equations that are true for all values of the variables, such as sin(A) = cos(90° - A)
Trigonometry
Sine, Cosine, and Tangent
- Sine (sin): The ratio of the opposite side to the hypotenuse in a right-angled triangle, calculated as sin(A) = opposite side / hypotenuse.
- Cosine (cos): The ratio of the adjacent side to the hypotenuse in a right-angled triangle, calculated as cos(A) = adjacent side / hypotenuse.
- Tangent (tan): The ratio of the opposite side to the adjacent side in a right-angled triangle, calculated as tan(A) = opposite side / adjacent side.
Angles and Triangles
- Right-angled triangle: A triangle with one right angle (90°), used as a basis for trigonometric calculations.
- Angle of elevation: The angle between the line of sight and the horizontal when looking up at an object, used to calculate trigonometric values.
- Angle of depression: The angle between the line of sight and the horizontal when looking down at an object, used to calculate trigonometric values.
- Reference angle: The acute angle between the terminal side of an angle and the x-axis, used to simplify trigonometric calculations.
Solving Triangles
- Pythagorean identity: A fundamental equation in trigonometry, sin^2(A) + cos^2(A) = 1, which relates the sine and cosine of an angle.
- Sine rule: A formula used to solve triangles, a / sin(A) = b / sin(B) = c / sin(C), where a, b, and c are side lengths and A, B, and C are angles.
- Cosine rule: A formula used to solve triangles, a^2 = b^2 + c^2 - 2bc * cos(A), where a, b, and c are side lengths and A is an angle.
- Trigonometric identities: Equations that are true for all values of the variables, such as sin(A) = cos(90° - A), used to simplify trigonometric calculations and solve problems.
Studying That Suits You
Use AI to generate personalized quizzes and flashcards to suit your learning preferences.
Description
Learn about sine, cosine, and tangent in right-angled triangles, including their definitions and formulas. Practice problems and questions on trigonometric ratios.
