Trigonometry

There are very few trigonometry questions on the ACT Mathematics Test. The questions test the basic trigonometric ratios which are related to right triangles.

Basic Trigonometric Concepts

The hypotenuse is the side that is opposite the right angle. Sometimes the graph or diagram shown in the question will have the triangle rotated, so make sure that you know where the right angle is and the hypotenuse, which is directly opposite the right angle.

SOHCAHTOA

• SINE (sin) = Opposite/Hypotenuse (SOH)

• COSINE (cos) = Adjacent/Hypotenuse (CAH)

• TANGENT (tan) = Opposite/Adjacent (TOA)

Advanced Trigonometric Concepts

Pythagorean Identities:

sin² θ + cos² θ = 1

1 + tan² θ = sec² θ

1 + cot² θ = csc² θ

Trigonometric Identities:

Radians

To change from degrees to radians, multiply the number of degrees by π/180. Conversely, to change from radians to degrees, multiply the number of radians by 180/π.