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## Basic Trigonometry

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### Basic Trigonometry Sine Cosine Tangent Locate indicated angle and classify sides in relation to it. Use proper equation and write the ratio. Use calculator to round ... – PowerPoint PPT presentation

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Title: Basic Trigonometry

1
Basic Trigonometry
• Sine
• Cosine
• Tangent

2
The Language of Trig
The target angle is either one of the acute
angles of the right triangle.
Hypotenuse
Opposite
target angle
?
3
Trig Equations
Hypotenuse
Opposite
target angle
?
opposite
?
sin
Hypotenuse
4
Trig Equations
Hypotenuse
Opposite
target angle
?
?
COS
Hypotenuse
5
Trig Equations
Hypotenuse
Opposite
target angle
?
?
opposite
TAN
SOH - CAH - TOA
6
Given sides, find requested ratios
• Locate indicated angle and classify sides in
relation to it.
• Use proper equation and write the ratio.
• Use calculator to round to the nearest
ten-thousandths place.

Hypotenuse
Opposite
Find sin, cos, and tan of ?A.
8.2
opposite
sin A
24.5
Hypotenuse
23.1
COS A
24.5
Hypotenuse
8.2
opposite
TAN A
23.1
7
Solving for the unknown
• Unknown on top..Multiply

x
sin 40
24
Calculator 24 (sin 40) 15.4
8
Solving for the unknown
• Unknown on bottom..Divide

24
sin 40
x
Calculator 24 ?(sin 40) 37.3
9
Solving for the unknown
• Unknown angle..use inverse

15.4
x
sin
24
Calculator 2nd sin-1 (15.4/24) 40
10
Solving problems using trig
• Choose your target angle and classify sides in
relation to it.
• Use proper equation and write the ratio placing
the unknown wherever it falls.
• SolveUnless directed otherwise, round sides to
nearest tenth and angles to nearest degree.

Hypotenuse
Opposite
sin
Opposite
Hypotenuse
h
sin 30
52.6
h 52.6(sin 30) 26.3
11
Angle of Elevation
The angle of elevation is always Measured from
the Horizontal UP It is always INSIDE the
triangle.
12
Angle of Depression
The angle of depression is always Measured from
the Horizontal DOWN It is usually OUTSIDE the
triangle.
x
?
?
However.because horizontal lines are parallel,
an angle of depression is equal to its alternate
interior angle of elevation.
13
Practice
h
opposite
TAN 67
h
Opposite
30m
67?
30m
h 30(tan 67)
70.7m
14
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.