Basic TrigonometryBasic Trigonometry

SineSine

Cosine Cosine

TangentTangent

The Language of Trig

The target angle is

either one of the acute

angles of the right triangle.

Trig Equations

Trig Equations

Trig Equations

Given sides, find requested ratios:• Locate indicated Locate indicated angle and classify angle and classify sides in relation to sides in relation to it.it.

• Use proper equation Use proper equation and write the ratio.and write the ratio.

• Use calculator to Use calculator to round to the nearest round to the nearest ten-thousandths ten-thousandths place.place.

Find sin, cos, and tan of A.

8.2

24.523.124.5

8.2

23.1

Solving for the unknown:Solving for the unknown:

• Unknown on top…..MultiplyUnknown on top…..Multiply

x

24

Calculator: 24 * (sin 40)= 15.4

Solving for the unknown:Solving for the unknown:

• Unknown on bottom…..DivideUnknown on bottom…..Divide

x

24

Calculator: 24 (sin 40)= 37.3

Solving for the unknown:Solving for the unknown:

• Unknown angle…..use inverseUnknown angle…..use inverse

x24

Calculator: 2nd sin-1 (15.4/24)= 40

15.4

Solving problems using trig:• Choose your target Choose your target angle and classify angle and classify sides in relation to it.sides in relation to it.

• Use proper equation Use proper equation and write the ratio and write the ratio placing the unknown placing the unknown wherever it falls.wherever it falls.

• Solve…Unless Solve…Unless directed otherwise, directed otherwise, round sides to nearest round sides to nearest tenth and angles to tenth and angles to nearest degree.nearest degree. h

52.6h = 52.6(sin 30)

= 26.3

Angle of ElevationAngle of Elevation

The angle of elevation is always Measured from the Horizontal UP…It is always INSIDE the triangle.

Angle of DepressionAngle of Depression

The angle of depression is always Measured from the Horizontal DOWN…It is usually OUTSIDE the triangle.

However….because horizontal lines are parallel, an angle of depression is equal to its alternate interior angle of elevation.

x

PracticePractice

6730m

hh

30m

h = 30(tan 67) =70.7m

From a point on the ground 25 feet from the foot of a tree, the angle of elevation of the top of the tree is 32º. Find to the nearest foot, the height of the tree.

25 ft32°

x ft

Hyp Opp Adj

x 16 ft 32°

25 ft

x ft