Right Triangle Trigonometry
Trigonometry is based upon ratios of the sides of righttriangles.
The ratio of sides in triangles with the same angles isconsistent. The size of the triangle does not matterbecause the triangles are similar (same shape differentsize).
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The six trigonometric functions of a right triangle,with an acute angle , are defined by ratios of two sidesof the triangle.
The sides of the right triangle are:
the side opposite the acute angle ,
the side adjacent to the acute angle ,
and the hypotenuse of the right triangle.
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The trigonometric functions are
sine, cosine, tangent, cotangent, secant, and cosecant.
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Trigonometric Functions
sin = cos = tan =
csc = sec = cot =
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Reciprocal Functions
Another way to look at it…
sin = 1/csc csc = 1/sin
cos = 1/sec sec = 1/cos
tan = 1/cot cot = 1/tan
Given 2 sides of a right triangle you should be able to findthe value of all 6 trigonometric functions.
Example:
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Standard Triangle with A, B, C, a, b, and c
Angles: capital letters (A, B, and C) or greek letters (θ, α)
Sides: lower case letters (a, b, c)
Same letters are opposite of each other.
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b c
C B
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Solve for all missing sides and angles if b = 5 and c = 10.Assume C is the right angle.
1st: Draw the triangle
2nd:Pick an angle to use as a reference
3rd: Label opposite, adjacent, and hypotenuse
4th: Start solving!
You are 330 feet from the base of a building. The angles ofelevation to the top and bottom of a flagpole on top of thebuilding are 55o and 53o. Find the height of the flag pole.
1st: Draw the picture
2nd: Solve for each triangle
3rd: Answer the question
•Exit slip time!
•Homework: Day 3 on assignment guide!
• (I have the dates wrong!)
•Quiz coming up on Friday
•(this is a change from the assignment guide)