Trigonometry & Applications Flashcards
9 cards from real Geometry practice questions. Tap to flip, then mark Knew It or Still Learning — missed cards come back until you master them.
Read the first 9 Trigonometry & Applications flashcards as text
What does sine (sin) represent in a right triangle?
Answer: Opposite over hypotenuse
In a right-angled triangle, the sine of an acute angle is defined as the ratio of the length of the side opposite the angle to the length of the hypotenuse. This relationship is a fundamental part of trigonometry, often remembered by the "SOH" in SOH-CAH-TOA. It helps relate angles to side lengths.
What does cosine (cos) represent in a right triangle?
Answer: Adjacent over hypotenuse
In a right-angled triangle, the cosine of an acute angle is defined as the ratio of the length of the side adjacent to the angle to the length of the hypotenuse. This trigonometric ratio is a key component of SOH-CAH-TOA, specifically the "CAH" part. It is used to find unknown side lengths or angles.
What does tangent (tan) represent in a right triangle?
Answer: Opposite over adjacent
In a right-angled triangle, the tangent of an acute angle is defined as the ratio of the length of the side opposite the angle to the length of the side adjacent to the angle. This ratio is represented by the "TOA" in the SOH-CAH-TOA mnemonic. It is particularly useful when the hypotenuse is not involved in the calculation.
What is the Pythagorean identity?
Answer: sin²θ + cos²θ = 1
The Pythagorean identity, sin²θ + cos²θ = 1, is a fundamental trigonometric identity derived directly from the Pythagorean theorem and the definitions of sine and cosine in a right triangle. It holds true for any angle θ and is widely used to simplify trigonometric expressions and solve equations.
Which function is used to find an angle given two sides?
Answer: Inverse functions like sin⁻¹
When you know the ratio of two sides in a right triangle (e.g., opposite/hypotenuse for sine), you use inverse trigonometric functions (arcsin, arccos, arctan) to find the measure of the angle itself. For example, if sin(θ) = 0.5, then θ = sin⁻¹(0.5) = 30 degrees. These functions essentially "undo" the regular trigonometric functions.
Which tool uses trigonometry in real life?
Answer: Surveying
Surveying extensively uses trigonometry to measure distances, angles, and elevations of land features. Surveyors apply trigonometric ratios to calculate unknown lengths and heights by measuring angles and known distances, which is essential for construction, mapping, and land management.
What is the unit circle used for?
Answer: To define trig functions for all angles
The unit circle is a circle with a radius of one unit centered at the origin of a coordinate plane. It provides a visual and conceptual framework for extending the definitions of trigonometric functions (sine, cosine, tangent) beyond acute angles in right triangles to all real numbers (angles), including obtuse, reflex, and negative angles.
What is the hypotenuse in a right triangle?
Answer: The side opposite the right angle
In a right-angled triangle, the hypotenuse is always the longest side and is specifically located directly opposite the 90-degree (right) angle. It is a crucial component in the Pythagorean theorem and the definitions of trigonometric ratios.
What is SOH-CAH-TOA?
Answer: A mnemonic for trig ratios
SOH-CAH-TOA is a mnemonic device used to remember the definitions of the three basic trigonometric ratios for a right triangle. SOH stands for Sine = Opposite/Hypotenuse, CAH for Cosine = Adjacent/Hypotenuse, and TOA for Tangent = Opposite/Adjacent. It's a helpful tool for students learning trigonometry.