When Do I use Sin, Cos or Tan?

Colonel Allen M. Morris
10 Mar 201622:53
EducationalLearning
32 Likes 10 Comments

TLDRThe video script is an informative guide on understanding when to use cosine, sine, or tangent in trigonometry. It explains the basics of right triangles, including the definitions of hypotenuse, opposite, and adjacent sides, and how these relate to the trigonometric functions. The video uses a 30-60-90 triangle to illustrate the concepts and provides examples of how to apply the functions to find missing angles or sides. It also introduces memory aids like 'Soho cahoots and toads' to help remember the functions: sine is opposite/hypotenuse, cosine is adjacent/hypotenuse, and tangent is opposite/adjacent. The script emphasizes the importance of understanding these relationships for solving problems in trigonometry.

Takeaways
  • 📐 Understanding the context: The video explains when to use cosine, sine, or tangent in the context of right triangles, focusing on their applications rather than their computation.
  • 🔢 Trigonometric functions: Trigonometric functions (sine, cosine, tangent) help in calculating unknown sides and angles in right triangles when given two pieces of information.
  • ✅ Right triangle properties: A right triangle has 90 degrees and two acute angles that sum up to 90 degrees, with the hypotenuse being the longest side opposite the right angle.
  • 📌 Triangle terminology: The sides adjacent to the right angle are called legs, and the longest side is the hypotenuse. The side opposite a given angle is referred to as the opposite side.
  • 📈 Ratios in 30-60-90 triangles: In a 30-60-90 triangle, the ratio of the side lengths is consistent, with the side opposite the 30-degree angle being half the length of the hypotenuse.
  • 🔍 Sine function: Sine (sin) is defined as the ratio of the length of the opposite side to the length of the hypotenuse.
  • 🌐 Cosine function: Cosine (cos) is defined as the ratio of the length of the adjacent side to the length of the hypotenuse.
  • 📐 Tangent function: Tangent (tan) is defined as the ratio of the length of the opposite side to the length of the adjacent side.
  • 🤔 Problem-solving strategy: To solve for missing sides or angles, one must identify which trigonometric function corresponds to the known and unknown values.
  • 💡 Memory aids: The video suggests using mnemonic devices like 'Soho cahoots and toads' or the traditional 'sohcahtoa' to remember the trigonometric functions: sine (opposite/hypotenuse), cosine (adjacent/hypotenuse), and tangent (opposite/adjacent).
Q & A
  • What is the main focus of the video?

    -The main focus of the video is to explain when to use cosine, sine, or tangent in the context of right triangles, rather than how to use them.

  • How many sides and angles are there in a right triangle?

    -A right triangle has three sides, with one being the hypotenuse, and two angles, both of which are acute and add up to 90 degrees.

  • What does the 'D' notation in a right triangle signify?

    -The 'D' notation signifies that the triangle contains a right angle, which is 90 degrees or a quarter of a circle.

  • What is the significance of knowing two things about a right triangle?

    -If you know two things about a right triangle, such as the lengths of two sides or the measure of an angle, you can calculate all the other sides, angles, area, and perimeter.

  • What are the names of the sides in a right triangle relative to an angle θ?

    -The side opposite to angle θ is called the opposite side, the side next to angle θ is called the adjacent side, and the longest side opposite the right angle is the hypotenuse.

  • What is the sine of 30 degrees in a 30-60-90 triangle?

    -In a 30-60-90 triangle, the sine of 30 degrees is a pure number equal to 1/2, representing the ratio of the length of the opposite side to the hypotenuse.

  • How does the video suggest remembering the trigonometric functions?

    -The video suggests using a memory device such as associating the first letters of sine, cosine, and tangent with the words 'Soho', 'cahoots', and 'toads' to remember their respective functions.

  • What is the tangent function in terms of sides and angles in a right triangle?

    -The tangent function is the ratio of the length of the opposite side to the length of the adjacent side, represented as tan(θ) = opposite/adjacent.

  • How can you find the hypotenuse if you know the angle and the length of the opposite side?

    -If you know the angle and the length of the opposite side, you can use the sine function to find the hypotenuse. The sine of the angle is equal to the opposite side length divided by the hypotenuse, allowing you to solve for the hypotenuse length.

  • What is the cosine function used for in a right triangle?

    -The cosine function is used to find the length of the adjacent side when you know the angle and the length of the hypotenuse. It is represented as cos(θ) = adjacent/hypotenuse.

  • How can you determine if your answer in trigonometry makes sense?

    -To determine if your answer makes sense, you should check if it aligns with the properties of a right triangle, such as the hypotenuse being the longest side and if the calculated angles sum up to 90 degrees.

Outlines
00:00
📚 Introduction to Trigonometry

This paragraph introduces the basics of trigonometry, focusing on the right triangle and its relationship with sine, cosine, and tangent. It emphasizes the importance of understanding when to use each function rather than their application. The concept of right triangles having 90 degrees and two acute angles that sum up to 90 degrees is explained. The paragraph also introduces the notation for right angles and unknown angles (denoted by theta). It explains the terms hypotenuse, opposite, and adjacent sides in the context of right triangles.

05:01
📐 Understanding Trigonometric Ratios

The paragraph delves into the concept of trigonometric ratios, specifically sine, cosine, and tangent, in the context of a 30-60-90 triangle. It explains how knowing the length of any two sides allows for the calculation of the third side and the angles. The ratios are described as pure numbers, with examples given for sine, cosine, and tangent at a 30-degree angle. The paragraph also discusses how these ratios can be used to find missing sides or angles in right triangles, given certain information.

10:04
🔢 Trigonometric Functions and Their Applications

This section further explores the application of trigonometric functions when the angle or sides are known. It explains how to use sine, cosine, and tangent to find missing lengths or angles in a right triangle. The paragraph uses examples to illustrate how these functions work, emphasizing the importance of understanding the relationships between sides and angles. It also touches on the concept of pure numbers in trigonometry and how they can be found using a calculator or charts.

15:04
📊 Using Charts and Algebra for Trigonometric Problems

The paragraph discusses the use of charts and algebraic methods to solve trigonometric problems. It explains how to find the hypotenuse or other sides of a right triangle when given an angle and the length of one side, using sine, cosine, or tangent. The process involves looking up values in charts or using a calculator and then applying algebra to find the unknowns. The paragraph also highlights the importance of checking the logic of the answer against the properties of right triangles.

20:06
🧠 Mnemonics for Remembering Trigonometric Functions

In this paragraph, the speaker shares a personal mnemonic device to remember the trigonometric functions: sine, cosine, and tangent. The mnemonic 'Soho cahoots and toads' is introduced to help recall that sine is the opposite side divided by the hypotenuse, cosine is the adjacent side divided by the hypotenuse, and tangent is the opposite side divided by the adjacent side. The speaker also mentions the traditional mnemonic 'sohcahtoa' and encourages the audience to find mnemonics that work best for them.

Mindmap
Keywords
💡Trigonometric Functions
Trigonometric functions are mathematical functions that relate the angles of a right triangle to the lengths of its sides. In the context of the video, these functions—sine, cosine, and tangent—are used to solve for missing angles or side lengths in right triangles. The video emphasizes the importance of understanding when to use each function based on the information given in a problem.
💡Right Triangles
A right triangle is a triangle in which one of the angles is a right angle (90 degrees). The video explains that in a right triangle, knowing two elements (angles or sides) allows the calculation of the remaining elements. The properties of right triangles are central to the discussion of trigonometric functions.
💡Hypotenuse
The hypotenuse is the longest side of a right triangle, which is opposite the right angle. The video clarifies that the hypotenuse remains constant regardless of how the triangle is rotated around the right angle, and it is always opposite to the right angle.
💡Acute Angles
Acute angles are angles that are less than 90 degrees. In a right triangle, there are two acute angles, and their sum is always 90 degrees. The video discusses how the trigonometric functions are applied to these angles to find unknown sides or angles.
💡Sine (sin)
The sine function, often abbreviated as sin, relates the ratio of the length of the side opposite an angle to the length of the hypotenuse in a right triangle. The video emphasizes the use of sine to find the unknown side lengths or angles in a right triangle when the angle and the length of the opposite side are known.
💡Cosine (cos)
The cosine function, often abbreviated as cos, is the ratio of the length of the adjacent side to the length of the hypotenuse in a right triangle. The video explains that cosine is used to find the unknown side lengths or angles when the angle and the length of the adjacent side are known.
💡Tangent (tan)
The tangent function, abbreviated as tan, is the ratio of the length of the side opposite an angle to the length of the adjacent side in a right triangle. The video describes using tangent to solve for the missing side or angle when the angle and the length of one of the other two sides are known.
💡Theta (θ)
Theta, represented by the Greek letter θ, is used to denote an unknown angle in a right triangle. The video explains that when the angle is not known, it is referred to as theta, and trigonometric functions are used to find its measure or related side lengths.
💡Opposite Side
The opposite side of an angle in a right triangle is the side that is directly across from the angle in question. The video discusses how the lengths of the opposite side are used in the sine and tangent functions to solve for unknown angles or other sides.
💡Adjacent Side
The adjacent side of an angle in a right triangle is the side that is next to the angle, not including the hypotenuse. The video explains that the cosine function uses the length of the adjacent side in relation to the hypotenuse, and the tangent function uses the length of the opposite side in relation to the adjacent side.
💡Memory Devices
Memory devices are techniques or strategies used to aid in the recall of information. In the video, the presenter shares personal mnemonic devices, such as 'Soho cahoots and toads', to remember the relationships between the trigonometric functions and the sides of a right triangle.
Highlights

The video explains when to use cosine, sine, or tangent in trigonometry.

Trigonometric functions are useful for calculating unknown sides and angles in right triangles.

A right triangle can be fully calculated with two known values (two sides or one side and an angle).

The symbol 'D' denotes a right angle (90 degrees) in a triangle.

Theta (θ) represents an unknown angle in a right triangle.

The hypotenuse is the longest side and is opposite the right angle in a right triangle.

The words 'opposite' and 'adjacent' refer to the sides next to and opposite the angle in question.

The sine function is the ratio of the length of the opposite side to the hypotenuse.

The cosine function is the ratio of the length of the adjacent side to the hypotenuse.

The tangent function is the ratio of the length of the opposite side to the adjacent side.

A 30-60-90 triangle has specific ratios that remain constant for all such triangles.

The sine, cosine, and tangent values are pure numbers and can be found on charts or calculators.

The video provides a mnemonic device (Soho, cahoots, toads) to remember the trigonometric functions.

Traditional mnemonic device is 'sohcahtoa' to remember the trigonometric functions.

The video includes practice problems and links to additional resources for learning trigonometry.

The interior angles of all triangles in the universe sum up to 180 degrees.

The hypotenuse remains the same regardless of how the triangle is rotated around it.

The video emphasizes the importance of checking if the calculated answer makes sense in the context of the problem.

Transcripts
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