Cosine

Welcome to episode 7 of the Geometry and Trigonometry course! In this installment, we explore Cosine, the essential sibling to the Sine function. We will define cosine using the familiar right-angled triangle, focusing on the relationship between the 'adjacent' side and the hypotenuse. You'll learn the popular 'SOH CAH TOA' mnemonic to easily remember this ratio. We then expand our understanding beyond simple triangles by visualizing cosine on the unit circle, where it represents the x-coordinate of a point. This episode also uncovers the fundamental relationship between sine and cosine as 'co-functions', explaining how they relate through complementary angles. By the end, you'll understand what cosine is and why it's a cornerstone of mathematics and science.

Check your understanding

These are the same multiple-choice questions you will see in the Quiz section after you listen to the episode. Use them here to preview or review the answers.

In a right-angled triangle, how is the cosine of an angle (θ) defined?

  1. The ratio of the opposite side to the hypotenuse.
  2. The ratio of the adjacent side to the hypotenuse.
  3. The ratio of the opposite side to the adjacent side.
  4. The length of the adjacent side.
  5. The product of the adjacent side and the hypotenuse.

On a unit circle (a circle with radius 1), what does the cosine of an angle typically represent?

  1. The y-coordinate of the point on the circle.
  2. The radius of the circle.
  3. The x-coordinate of the point on the circle.
  4. The circumference of the circle.
  5. The angle itself.

Which of the following statements correctly describe the relationship between sine and cosine?

  1. cos(θ) = sin(90° - θ)
  2. cos(30°) has the same value as sin(60°).
  3. Sine and cosine are called co-functions because they are related by complementary angles.
  4. cos(θ) is always greater than sin(θ).
  5. cos(θ) = sin(θ) for all angles.

The mnemonic 'SOH CAH TOA' is often used to remember trigonometric ratios. What does the 'CAH' part stand for?

  1. Cosine is Adjacent over Hypotenuse.
  2. Cosine and Hypotenuse are Adjacent.
  3. Cosine is Adjacent times Hypotenuse.
  4. Cosine is Hypotenuse over Adjacent.
  5. Cosine is Adjacent plus Hypotenuse.

Which two sides of a right-angled triangle are used in the ratio to calculate the cosine of an angle?

  1. The opposite side
  2. The hypotenuse
  3. The adjacent side
  4. The shortest side

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