Trig review

Front

What is the tangent ratio in a right triangle?

Back

The tangent ratio is defined as the ratio of the length of the opposite side to the length of the adjacent side. It is expressed as tan(θ) = opposite/adjacent.

Front

How do you solve for a side using the tangent function?

Back

To solve for a side using the tangent function, rearrange the equation tan(θ) = opposite/adjacent to find the unknown side. For example, if tan(58) = x/11, then x = 11 * tan(58).

Front

What is the sine ratio in a right triangle?

Back

The sine ratio is defined as the ratio of the length of the opposite side to the length of the hypotenuse. It is expressed as sin(θ) = opposite/hypotenuse.

Front

What is the cosine ratio in a right triangle?

Back

The cosine ratio is defined as the ratio of the length of the adjacent side to the length of the hypotenuse. It is expressed as cos(θ) = adjacent/hypotenuse.

Front

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

Back

To find the length of a side using the sine function, rearrange the equation sin(θ) = opposite/hypotenuse to find the unknown side. For example, if sin(30) = x/10, then x = 10 * sin(30).

Front

What is the relationship between the sides of a 30-60-90 triangle?

Back

In a 30-60-90 triangle, the lengths of the sides are in the ratio 1:√3:2. The side opposite the 30° angle is the shortest, the side opposite the 60° angle is √3 times the shortest, and the hypotenuse is twice the shortest.

Front

What is the relationship between the sides of a 45-45-90 triangle?

Back

In a 45-45-90 triangle, the lengths of the legs are equal, and the hypotenuse is √2 times the length of each leg.

Front

How do you calculate the angle using the tangent function?

Back

To calculate the angle using the tangent function, use the inverse tangent function: θ = tan⁻¹(opposite/adjacent).

Front

What is the formula for finding the hypotenuse in a right triangle?

Back

The formula for finding the hypotenuse in a right triangle is derived from the Pythagorean theorem: c² = a² + b², where c is the hypotenuse and a and b are the other two sides.

Front

What is the sine rule in trigonometry?

Back

The sine rule states that in any triangle, the ratio of a side length to the sine of its opposite angle is constant: a/sin(A) = b/sin(B) = c/sin(C).