Trigonometric Ratios Of Complements
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4Math 2 Unit 2 Right Triangle Trigonometry
Name:
TRIGONOMETRIC RATIOS OF COMPLEMENTS
GPStandard MM2G2
Students will define and apply sine, cosine and tangent ratios to right triangles.
a.
Discover the relationship of the trigonometric ratios for similar triangles.
b.
Explain the relationship between the trigonometric ratios of complementary angles.
c.
Solve application problems using the trigonometric ratios.
EQ: How do we explain the relationship of trigonometric ratios of complementary angles?
Let (theta) be an acute angle of a right triangle. How can we write the angle complement to ?
Suppose we have right triangle with an acute angle and short leg a, long leg b and hypotenuse c. How
can we complete a SOHCAHTOA chart for and its complement.
The set of numbers { 5, 12, 13 } is an example of a Pythagorean triple. Why?
How can we use this Pythagorean triple to help us label the given triangle and complete the chart?
sin
cos
tan
VISUAL
sin 90
cos 90
tan 90
The set of numbers { 25, 7, 24 } is an example of a Pythagorean triple. However, a student argued that
2
2
674
it’s not because the student derived that
25
7
674
and
7
. How would you prove this
student is wrong?
How can we use this Pythagorean triple to help us label the given triangle and complete the chart?
sin
cos
tan
VISUAL
sin 90
cos 90
tan 90
The set of numbers { 15, 17, 8 } is an example of a Pythagorean triple. A student completed the
chart below but several students said “Hey! you did this wrong.” How can you support the students’
argument by showing what the student is supposed to do?
sin
cos
tan
sin
cos
tan
8
17
8
15
15
17
What does this problem tell you about the hypotenuse of a right triangle?
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