Trigonometry

Front

What is Trigonometry?

Back

Trigonometry is a branch of mathematics that studies the relationships between the angles and sides of triangles, particularly right triangles.

Front

What is the Pythagorean Theorem?

Back

The Pythagorean Theorem states that in a right triangle, the square of the length of the hypotenuse (c) is equal to the sum of the squares of the lengths of the other two sides (a and b). Formula: a² + b² = c².

Front

What are the primary trigonometric ratios?

Back

The primary trigonometric ratios are sine (sin), cosine (cos), and tangent (tan). They are defined as follows: sin(θ) = opposite/hypotenuse, cos(θ) = adjacent/hypotenuse, tan(θ) = opposite/adjacent.

Front

How do you find the sine of an angle?

Back

To find the sine of an angle in a right triangle, divide the length of the side opposite the angle by the length of the hypotenuse.

Front

How do you find the cosine of an angle?

Back

To find the cosine of an angle in a right triangle, divide the length of the adjacent side by the length of the hypotenuse.

Front

How do you find the tangent of an angle?

Back

To find the tangent of an angle in a right triangle, divide the length of the side opposite the angle by the length of the adjacent side.

Front

What is the relationship between sine and cosine?

Back

The sine and cosine functions are related through the identity: sin²(θ) + cos²(θ) = 1.

Front

What is an angle of elevation?

Back

An angle of elevation is the angle formed by the horizontal line and the line of sight to an object above the horizontal.

Front

What is an angle of depression?

Back

An angle of depression is the angle formed by the horizontal line and the line of sight to an object below the horizontal.

Front

How do you solve for an unknown angle using inverse trigonometric functions?

Back

To solve for an unknown angle, use the inverse trigonometric functions: θ = sin⁻¹(opposite/hypotenuse), θ = cos⁻¹(adjacent/hypotenuse), θ = tan⁻¹(opposite/adjacent).