Geometry Topic 8

Hypotenuse

The side of a right triangle opposite the right angle

Opposite side

The leg of a right triangle across from the marked acute angle

Adjacent side

The leg that forms the marked acute angle (next to the angle)

Greek letter commonly used to represent an angle in trigonometry

θ (theta)

sin(θ) formula

opposite / hypotenuse

cos(θ) formula

adjacent / hypotenuse

tan(θ) formula

opposite / adjacent

SOH CAH TOA mnemonic

Sine = Opposite/Hypotenuse, Cosine = Adjacent/Hypotenuse, Tangent = Opposite/Adjacent

Complementary angles

Two angles whose measures add up to 90°

Relationship between sine and cosine of complementary angles

sin(A) = cos(B) when A + B = 90°

Cosine identity for sine using one angle

sin(θ) = cos(90° − θ)

Trig ratios used to find side lengths

Sine, cosine, and tangent

Which trig ratio uses opposite and hypotenuse

Sine

Which trig ratio uses adjacent and hypotenuse

Cosine

Which trig ratio uses opposite and adjacent

Tangent

Inverse sine

sin⁻¹ or arcsin

Inverse cosine

cos⁻¹ or arccos

Inverse tangent

tan⁻¹ or arctan

Purpose of inverse trig functions

To find an angle when the side ratio is known

Calculator mode used for most trig problems

Degree mode

Angle of elevation

The angle measured upward from a horizontal line of sight

Angle of depression

The angle measured downward from a horizontal line of sight

Relationship between angles of elevation and depression

They are equal due to alternate interior angles

Common special angles in trigonometry

0°, 30°, 45°, 60°, 90°

45-45-90 triangle side ratio

1 : 1 : √2

30-60-90 triangle side ratio

1 : √3 : 2

sin(30°)

1/2

cos(30°)

√3 / 2

sin(45°)

√2 / 2

cos(45°)

√2 / 2

sin(60°)

√3 / 2

cos(60°)

1/2

sin(0°)

0

cos(0°)

1

sin(90°)

1

cos(90°)

0