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): c² = a² + b².

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 in a right triangle?

Back

To find the sine of an angle θ, divide the length of the side opposite the angle by the length of the hypotenuse: sin(θ) = opposite/hypotenuse.

Front

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

Back

To find the cosine of an angle θ, divide the length of the side adjacent to the angle by the length of the hypotenuse: cos(θ) = adjacent/hypotenuse.

Front

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

Back

To find the tangent of an angle θ, divide the length of the side opposite the angle by the length of the side adjacent to the angle: tan(θ) = opposite/adjacent.

Front

What is the relationship between sine and cosine?

Back

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

Front

What is an angle's reference angle?

Back

The reference angle is the acute angle formed by the terminal side of an angle and the x-axis. It is always positive and less than 90 degrees.

Front

What is the unit circle?

Back

The unit circle is a circle with a radius of 1 centered at the origin of a coordinate plane. It is used to define trigonometric functions for all angles.

Front

How do you convert degrees to radians?

Back

To convert degrees to radians, multiply the degree measure by π/180. For example, 180 degrees = π radians.