What is the relationship between sine, cosine, and tangent?

The relationship can be expressed as: $$\text{tan} A = \frac{\text{sin} A}{\text{cos} A}$$ .

If sin A = 0.5, what is the angle A?

Angle A is 30 degrees (or $$\frac{\text{\text{pi}}}{6}$$ radians).

If cos A = 0.6, what is the angle A?

Angle A is approximately 53.13 degrees (or $$\frac{5\text{\text{pi}}}{12}$$ radians).

What is the Pythagorean identity involving sine and cosine?

The Pythagorean identity states that: $$\text{sin}^2 A + \text{cos}^2 A = 1$$ .

How do you apply trigonometric ratios to find a missing side in a right triangle?

Use the appropriate trigonometric ratio (sin, cos, or tan) based on the known sides and the angle to set up an equation and solve for the missing side.

What is the sine rule in trigonometry?

The sine rule states that in any triangle, the ratio of a side length to the sine of its opposite angle is constant: $$\frac{a}{\text{sin} A} = \frac{b}{\text{sin} B} = \frac{c}{\text{sin} C}$$ .

What is the cosine rule in trigonometry?

The cosine rule relates the lengths of the sides of a triangle to the cosine of one of its angles: $$c^2 = a^2 + b^2 - 2ab \text{cos} C$$ .

What is the purpose of using trigonometric ratios in real-life applications?

Trigonometric ratios are used in various fields such as physics, engineering, and architecture to solve problems involving angles and distances.

Flashcard #4: Trigonometric Ratios Flashcards

Student preview

15 questions

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1.

FLASHCARD QUESTION

Front

What is the definition of a trigonometric ratio?

Back

A trigonometric ratio is a ratio of the lengths of two sides of a right triangle. The primary trigonometric ratios are sine, cosine, and tangent.

Tags

CCSS.HSG.SRT.C.6

2.

FLASHCARD QUESTION

Front

What is the sine ratio?

Back

Tags

CCSS.HSG.SRT.C.6

3.

FLASHCARD QUESTION

Front

What is the cosine ratio?

Back

Tags

CCSS.HSG.SRT.C.6

4.

FLASHCARD QUESTION

Front

What is the tangent ratio?

Back

Tags

CCSS.HSG.SRT.C.6

5.

FLASHCARD QUESTION

Front

How do you find the sine of an angle in a right triangle?

Back

To find the sine of an angle, divide the length of the side opposite the angle by the length of the hypotenuse.

Tags

CCSS.HSG.SRT.C.6

6.

FLASHCARD QUESTION

Front

How do you find the cosine of an angle in a right triangle?

Back

To find the cosine of an angle, divide the length of the side adjacent to the angle by the length of the hypotenuse.

Tags

CCSS.HSG.SRT.C.6

7.

FLASHCARD QUESTION

Front

How do you find the tangent of an angle in a right triangle?

Back

To find the tangent of an angle, divide the length of the side opposite the angle by the length of the side adjacent to the angle.

Tags

CCSS.HSG.SRT.C.6

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