Trig Ratios

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 calculate the sine of an angle in a right triangle?

Back

To calculate the sine of an angle θ in a right triangle, divide the length of the side opposite the angle by the length of the hypotenuse: sin(θ) = opposite/hypotenuse.

Front

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

Back

To calculate the cosine of an angle θ in a right triangle, divide the length of the side adjacent to the angle by the length of the hypotenuse: cos(θ) = adjacent/hypotenuse.

Front

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

Back

To calculate the tangent of an angle θ in a right triangle, 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 relationship between sine and cosine can be expressed using the Pythagorean identity: sin²(θ) + cos²(θ) = 1.

Front

What is the value of sin(30°)?

Back

The value of sin(30°) is 1/2.

Front

What is the value of cos(60°)?

Back

The value of cos(60°) is 1/2.

Front

What is the value of tan(45°)?

Back

The value of tan(45°) is 1.

Front

How can you find the value of a trigonometric ratio using a right triangle?

Back

To find the value of a trigonometric ratio using a right triangle, identify the lengths of the sides relative to the angle of interest and apply the definitions of sine, cosine, or tangent.

Front

What is the sine rule in trigonometry?

Back

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