TRIGONOMETRY

• Find trigonometric ratios using right triangles

• Solve problems using trigonometric ratios

Sextant

TRIGONOMETRIC RATIOS

TRIGONOMETRY comes from two Greek terms:

– trigon, meaning triangle

– metron, meaning measure

TRIGONOMETRY comes from two Greek terms:

– trigon, meaning triangle

– metron, meaning measure

TRIGONOMETRIC RATIOS

TRIGONOMETRY comes from two Greek terms:

– trigon, meaning triangle

– metron, meaning measure

TRIGONOMETRY comes from two Greek terms:

– trigon, meaning triangle

– metron, meaning measure

A ratio of the lengths of sides of a right triangle is called a TRIGONOMETRIC RATIO.A ratio of the lengths of sides of a right triangle is called a TRIGONOMETRIC RATIO.

TRIGONOMETRIC RATIOS

The three most common trigonometric ratios are:

• Sine• Cosine• Tangent

Key Concept Trigonometric Ratios

hypotenuse

A

B

C

Begin with a right triangle

Key Concept Trigonometric Ratios

sine of A =measure of leg opposite A

measure of hypotenuse

hypotenuse leg opposite

A

leg opposite BA

B

C

Key Concept Trigonometric Ratios

sine of A =measure of leg opposite A

measure of hypotenuse

hypotenuse leg opposite

A

leg opposite BA

B

C

sin A = BCAB

Key Concept Trigonometric Ratios

sine of A =measure of leg opposite A

measure of hypotenuse

hypotenuse leg opposite

A

leg opposite BA

B

C

sin A = BCAB

sine of B =measure of leg opposite B

measure of hypotenuse

Key Concept Trigonometric Ratios

sine of A =measure of leg opposite A

measure of hypotenuse

hypotenuse leg opposite

A

leg opposite BA

B

C

sin A = BCAB

sine of B =measure of leg opposite B

measure of hypotenusesin B = AC

AB

Key Concept Trigonometric Ratios

cosine of A =measure of leg adjacent to A

measure of hypotenuse

hypotenuse

leg adjacent to AA

B

C

Key Concept Trigonometric Ratios

cosine of A =measure of leg adjacent to A

measure of hypotenuse

hypotenuse

leg adjacent to AA

B

C

cos A = ACAB

Key Concept Trigonometric Ratios

cosine of A =measure of leg adjacent to A

measure of hypotenuse

hypotenuse leg adjacent to

B

leg adjacent to AA

B

C

cos A = ACAB

cosine of B =measure of leg adjacent to B

measure of hypotenuse

Key Concept Trigonometric Ratios

cosine of A =measure of leg adjacent to A

measure of hypotenuse

hypotenuse leg adjacent to

B

leg adjacent to AA

B

C

cos A = ACAB

cosine of B =measure of leg adjacent to B

measure of hypotenusecos B = BC

AB

Key Concept Trigonometric Ratios

tangent of A =measure of leg opposite A

measure of leg adjacent to A

hypotenuseleg opposite

A and adjacent to

B

leg adjacent to A and opposite B

A

B

C

Key Concept Trigonometric Ratios

tangent of A =measure of leg opposite A

measure of leg adjacent to A

hypotenuseleg opposite

A and adjacent to

B

leg adjacent to A and opposite B

A

B

C

tan A = BCAC

Key Concept Trigonometric Ratios

tangent of A =measure of leg opposite A

measure of leg adjacent to A

hypotenuseleg opposite

A and adjacent to

B

leg adjacent to A and opposite B

A

B

C

tan A = BCAC

tangent of B =measure of leg opposite B

measure of leg adjacent to B

Key Concept Trigonometric Ratios

tangent of A =measure of leg opposite A

measure of leg adjacent to A

hypotenuseleg opposite

A and adjacent to

B

leg adjacent to A and opposite B

A

B

C

tan A = BCAC

tangent of B =measure of leg opposite B

measure of leg adjacent to Btan B = AC

BC

Reading Math

SOH – CAH – TOA

sin A =

cos A =

tan A =

opphypadjhypoppadj

TRIGONOMETRIC RATIOS

The three most common trigonometric ratios are:• Sine• Cosine• Tangent

Sine function key

Cosine function key

Tangent function key