Podcast
Questions and Answers
In a right-angled triangle, which side is always opposite the right angle?
In a right-angled triangle, which side is always opposite the right angle?
- Base
- Adjacent
- Hypotenuse (correct)
- Opposite
The sine of an angle in a right-angled triangle is defined as the ratio of the adjacent side to the hypotenuse.
The sine of an angle in a right-angled triangle is defined as the ratio of the adjacent side to the hypotenuse.
False (B)
What is the formula to calculate the midpoint (M) of a line segment with endpoints $(x_1, y_1)$ and $(x_2, y_2)$?
What is the formula to calculate the midpoint (M) of a line segment with endpoints $(x_1, y_1)$ and $(x_2, y_2)$?
- $M = (\frac{x_1 - x_2}{2}, \frac{y_1 - y_2}{2})$
- $M = (\frac{x_1 + y_1}{2}, \frac{x_2 + y_2}{2})$
- $M = (x_2 - x_1, y_2 - y_1)$
- $M = (\frac{x_1 + x_2}{2}, \frac{y_1 + y_2}{2})$ (correct)
Given a right-angled triangle with an angle $\theta$, where the opposite side is 5 and the adjacent side is 12, what is the value of $\tan(\theta)$?
Given a right-angled triangle with an angle $\theta$, where the opposite side is 5 and the adjacent side is 12, what is the value of $\tan(\theta)$?
Two points are located at (2, 3) and (6, 8) on the Cartesian plane. What is the gradient/slope of the line segment joining these points?
Two points are located at (2, 3) and (6, 8) on the Cartesian plane. What is the gradient/slope of the line segment joining these points?
Rounding 3.14159 to 3 significant figures results in 3.142.
Rounding 3.14159 to 3 significant figures results in 3.142.
What is the distance between the points (1, 2) and (4, 6) on the Cartesian plane?
What is the distance between the points (1, 2) and (4, 6) on the Cartesian plane?
Simplify $\sqrt{27}$ into the form $a\sqrt{b}$ where a and b are integers and b is as small as possible.
Simplify $\sqrt{27}$ into the form $a\sqrt{b}$ where a and b are integers and b is as small as possible.
What is the meaning of gradient?
What is the meaning of gradient?
Flashcards
What is the hypotenuse?
What is the hypotenuse?
The side opposite the right angle in a right-angled triangle.
What is the adjacent side?
What is the adjacent side?
The side next to the angle (not the hypotenuse).
What is Sine (sin θ)?
What is Sine (sin θ)?
The ratio of the opposite side to the hypotenuse.
What is Cosine (cos θ)
What is Cosine (cos θ)
Signup and view all the flashcards
What is Tangent (tan θ)?
What is Tangent (tan θ)?
Signup and view all the flashcards
What is an Interval?
What is an Interval?
Signup and view all the flashcards
What is Gradient/Slope?
What is Gradient/Slope?
Signup and view all the flashcards
What is the midpoint?
What is the midpoint?
Signup and view all the flashcards
What is rounding?
What is rounding?
Signup and view all the flashcards
What is Surd?
What is Surd?
Signup and view all the flashcards
Study Notes
- These questions cover trigonometry, linear relationships, numbers of any magnitude, and indices.
- They're designed to assess your understanding of key concepts and your ability to apply them.
Trigonometry
- Trigonometric ratios remain constant for a given angle within similar right-angled triangles.
- In a right-angled triangle: the hypotenuse is opposite the right angle, the adjacent side is next to the given angle, and the opposite side is across from the given angle.
- Sine (sin) = Opposite / Hypotenuse
- Cosine (cos) = Adjacent / Hypotenuse
- Tangent (tan) = Opposite / Adjacent
- Find approximations of trigonometric ratios using calculators or tables for a given angle.
- Use inverse trigonometric functions (sin⁻¹, cos⁻¹, tan⁻¹) on digital tools to find the angle size when given a trigonometric ratio.
Right-Angled Triangle Problems
- Use trigonometric ratios to calculate unknown side lengths when an angle and one side are known.
- Apply trigonometry to find unknown angles when two side lengths are known.
- Solve real-world problems using trigonometric ratios in right-angled triangles.
Linear Relationships
- An interval on the Cartesian plane can be the hypotenuse of a right-angled triangle.
- Gradient (slope) = Rise / Run
- Positive gradients indicate an increasing line; negative gradients indicate a decreasing line.
- Horizontal lines have a gradient of 0; vertical lines have undefined gradients.
- The midpoint of an interval is the average of the x-coordinates and the average of the y-coordinates of the endpoints.
- Midpoint Formula: ((x₁+x₂)/2, (y₁+y₂)/2)
- Apply Pythagoras' theorem (a² + b² = c²) to calculate the distance between two points on the Cartesian plane.
Numbers of Any Magnitude
- Estimation involves rounding numbers to a specific level of accuracy.
- Round numbers to a given number of significant figures.
Indices
- Surds are irrational expressions in the form √a, where a is a rational number, n is an integer, n > 1, and a^(1/n) is irrational.
- A surd represents an exact value, whereas its decimal approximation is rounded.
Distance Formula
- Distance = √((x₂ - x₁)² + (y₂ - y₁)²)
- This formula is derived from Pythagoras' theorem.
Studying That Suits You
Use AI to generate personalized quizzes and flashcards to suit your learning preferences.
Description
Explore trigonometry, linear relationships, and indices. Learn about trigonometric ratios, right-angled triangles, and how to use them to calculate unknown side lengths. Understand numbers of any magnitude.
