Trigonometric Identities
Trigonometric Identities
•Reciprocal Identities
2
sin 1
csc
cos 1
sec
tan 1
cot
csc 1
sin
sec 1
cos
cot 1
tan
Trigonometric Identities
•Quotient Identities
3
tan sincos
cot cossin
Trigonometric Identities
•Pythagorean Identities
4
sin2 cos2 1
1 tan2 sec2
1 cot 2 csc2
Note: sin2 is (sin )2 not sin (2)
Example 5
Use trigonometric identities to transform one side of the equation into the other.
•cossec=1
•(sec+tan)(sec-tan)=1
5
Homework Practice
6
Surveying
•A surveyor is standing 50 ft from the base of a large tree. The surveyor measures the angle of elevation to the top of the tree as 71.5°. How tall is the tree?
7
River Walk
• You are 200 yards from a river. Rather than walking directly to the river, you walk 400 yards along a straight path to the river’s edge. Find the acute angle ө between this path and the river’s edge.
8
Skateboarding
•Find the length c of the skateboard ramp.
9
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