3.1 Relating right triangle trigonometry to the sine, cosine, and tangent functions

• What is the ratio that defines cosine (cos)?

  Adjacent / Hypotenuse
• What do sine, cosine, and tangent relate in a right triangle?

  Angles and side ratios
• Arrange the trigonometric functions in order of their ratios:

  1️⃣ Sine (sin): Opposite / Hypotenuse

  2️⃣ Cosine (cos): Adjacent / Hypotenuse

  3️⃣ Tangent (tan): Opposite / Adjacent
• Cosine (cos θ) is calculated as the ratio of the adjacent side to the hypotenuse
• The sine function is defined as the ratio of the opposite side to the hypotenuse.
• What do the formulas for trigonometric functions allow you to calculate?

  Trigonometric function values
• Match the trigonometric function with its definition:

  Sine (sin θ) ↔️ Opposite / Hypotenuse

  Cosine (cos θ) ↔️ Adjacent / Hypotenuse

  Tangent (tan θ) ↔️ Opposite / Adjacent
• What is the primary focus of right triangle trigonometry?

  Relationships in right triangles
• Tangent (tan) is the ratio of the opposite side to the adjacent side.

  True
• Sine (sin) is defined as the ratio of the opposite side to the hypotenuse
• Tangent (tan θ) is equal to the opposite side divided by the adjacent side.


  True
• What is the cosine function defined as?

  Adjacent / Hypotenuse
• The sine, cosine, and tangent functions are fundamental trigonometric ratios that relate angles to the sides of a right triangle.
• What is the formula for the tangent function in terms of triangle sides?

  Opposite / Adjacent
• Steps to solve problems using sine, cosine, and tangent:

  1️⃣ Identify the angle and sides involved

  2️⃣ Choose the appropriate trigonometric function

  3️⃣ Set up the equation

  4️⃣ Solve for the unknown side or angle

  5️⃣ Check the answer for reasonableness
• Sine (sin) is defined as the ratio of the opposite side to the hypotenuse
• Match each trigonometric function with its correct definition:

  Sine (sin) ↔️ Opposite / Hypotenuse

  Cosine (cos) ↔️ Adjacent / Hypotenuse

  Tangent (tan) ↔️ Opposite / Adjacent
• Cosine (cos) is the ratio of the adjacent side to the hypotenuse.

  True
• What is the formula for sine (sin θ)?

  Opposite / Hypotenuse
• What is right triangle trigonometry primarily concerned with?

  Relationships in right triangles
• The tangent function is the ratio of the opposite side to the adjacent side.

  True
• What is the sine of an angle defined as in terms of triangle sides?

  Opposite / Hypotenuse
• The trigonometric formulas directly relate angles to the lengths of the triangle sides.

  True
• In the example given, what is the value of side x in the right triangle?

  5