Using Trig Ratios to find sides and angles and Special Triangles

What is the importance of special triangles in trigonometry?

• They provide exact values for trigonometric ratios, making calculations easier.

• They are used to derive the Pythagorean theorem.

• They help in solving linear equations.

• They are only applicable in geometry, not trigonometry.

Define Cosine (cos) in a right triangle.

• Cosine is the ratio of the length of the opposite side to the length of the hypotenuse.

• Cosine is the ratio of the length of the adjacent side to the length of the hypotenuse.

• Cosine is the ratio of the length of the hypotenuse to the length of the adjacent side.

• Cosine is the ratio of the length of the opposite side to the length of the adjacent side.

How do you find the length of a side using sine?

• Use the formula: opposite = hypotenuse * sin(angle).

• Use the formula: adjacent = hypotenuse * cos(angle).

• Use the formula: hypotenuse = opposite / sin(angle).

• Use the formula: opposite = adjacent * tan(angle).

Define Tangent (tan) in a right triangle.

• Tangent is the ratio of the length of the opposite side to the length of the adjacent side.

• Tangent is the sum of the lengths of the opposite and adjacent sides.

• Tangent is the product of the lengths of the opposite and adjacent sides.

• Tangent is the difference between the lengths of the opposite and adjacent sides.

How do you find the length of a side using tangent?

• Use the formula: opposite = adjacent * tan(angle).

• Use the formula: opposite = adjacent / tan(angle).

• Use the formula: opposite = tan(angle) / adjacent.

• Use the formula: opposite = adjacent + tan(angle).

What is the Pythagorean theorem?

• In a right triangle, a² + b² = c², where c is the hypotenuse.

• In any triangle, the sum of the angles equals 180 degrees.

• The area of a circle is πr², where r is the radius.

• The relationship between the sides of a triangle is given by a² + b² = c, where c is the longest side.

How do you find an angle using the tangent ratio?

• Use the inverse tangent function: angle = tan⁻¹(opposite/adjacent).

• Multiply the opposite side by the adjacent side.

• Add the opposite and adjacent sides together.

• Use the sine function: angle = sin⁻¹(opposite/hypotenuse).

What is the special triangle ratio for a 30-60-90 triangle?

• 1 : 1 : 1

• 1 : √2 : 2

• 1 : √3 : 2

• 1 : 2 : √3

How do you find an angle using the sine ratio?

• Use the inverse sine function: angle = sin⁻¹(opposite/hypotenuse).

• Multiply the sine ratio by 90 degrees.

• Add the opposite and adjacent sides to find the angle.

• Use the cosine function: angle = cos⁻¹(adjacent/hypotenuse).

What are the primary trigonometric ratios?

• Sine (sin), Cosine (cos), Tangent (tan)

• Secant (sec), Cosecant (csc), Cotangent (cot)

• Sine (sin), Cosecant (csc), Secant (sec)

• Tangent (tan), Cotangent (cot), Secant (sec)