8-3 trigonometry
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8-3 Trigonometry. Learning Goal To use the sine, cosine, and tangent ratios to determine side lengths and angle measures in right triangles. - PowerPoint PPT PresentationTRANSCRIPT
8-3
Trigonometry
Learning Goal
To use the sine, cosine, and tangent ratios to determine side lengths and angle measures in
right triangles.
For the remainder of the year your calculator must be in
degree mode. All your answers will be wrong if it is not in degree
mode.
Get out your calculators now. Mr. Bradford will show you.
Do not copy.
Trigonometric Ratio
A ratio of the lengths of sides of a right triangle.
Do not copy.
Examples: sine, cosine and tangent.
Abbreviations: sin, cos and tan.
Some Old Horse Came A Hopping Through Our Alley
Some Old Horse
Sin Θ = oppositehypotenuse
Came A Hopping
Cos Θ = adjacenthypotenuse
Through Our Alley
Tan Θ =oppositeadjacent
Θ is the measure of an acute angle in a right triangle.
Step 1Label the Hypotenuse.(across from the right angle)
43˚
x
10
hyp
Step 2Put an arc over the angle that has a number or variable with a degree symbol.
43˚
x
10
hyp
Step 3Label the other side the arc touches: Adjacent.
43˚
x
10
hyp
adj
Step 4Label the remaining side: Opposite.
43˚
x
10
hyp
adj
opp
Step 5Decide if sin, cos or tan.
43˚
x
10
hyp
adj
opp
Step 6Create equation.
43˚
x
10
hyp
adj
opp
tan 43 = —10x
Step 7Solve.
tan 43 = —10x
Step 7Solve.
tan 43 = —10x
.9325 = —10x
Step 7Solve.
tan 43 = —10x
.9325 = —10x( )x( )x
Step 7Solve.
tan 43 = —10x
.9325 = —10x
.9325x = 10
( )x( )x
Step 7Solve.
tan 43 = —10x
.9325 = —10x
.9325x = 10
( )x( )x
.9325.9325
Step 7Solve.
tan 43 = —10x
.9325 = —10x
.9325x = 10
x = 10.7
( )x( )x
.9325.9325
Lets try another.
x˚
12
16
Lets try another.sin x = —12
16
Lets try another.sin x = —
sin x = .75
1216
Lets try another.sin x = —
sin x = .75
1216
sin-1(sin x) = sin-1.75
Lets try another.sin x = —
sin x = .75
1216
sin-1(sin x) = sin-1.75
Lets try another.sin x = —
sin x = .75
1216
sin-1(sin x) = sin-1.75
x = 48.6
Trigonometry Worksheet
5 Points: 100% Complete 4 Points: 80% Complete 3 Points: 60% Complete 2 Points: 40% Complete
1 Point: 20% Complete