Pythagorean Identities
Find the exact value of the remaining trig functions
tan A = -1/3, sin A>0
1
By Pythagorean theorem: x²+y²=1
y
x
Since x= cosine & y= sine, we can say: cos² + sin² = 1
sin A = 1/( 10 ) csc A= 10
( 10 )/10
cos A= -3/( 10 ) sec A= -( 10 )/3
= (-3 10 )/10 cot A= -3
You have five minutes to do these problems as they might be on the final!
A Real World Example
To get the other identities:
Find the exact value of this expression:
sin (- /12) csc (25 /12)
Divide cos² + sin² = 1 by sin²
Page 393 in the textbook:
53) sec = 2
75) sec (- /6)
83) cos 400 sec 40
85) sin (- /12) csc (25 /12)
You get: cot² + 1 = csc²
Divide cos² + sin² = 1 by cos²
Video Explanation
a) 1
b) -1
c) 0
75) sec (- /6)
.
83) cos 400 sec 40
.
53) sec = 2, sin <0
85) sin (- /12) csc (25 /12)
You get: 1 + tan² = sec²
180
.
cos = 1/2
sin = - 3
-30
.
(1/ (cos 40 ))
=
cos (360 + 40 )
=
.
sin (-15 ) csc (360 +15 )
=
6
.
cos 40
=
(1/ (cos 40 ))
.
- sin (15 )
( 1/ (sin 15 ))
2
=
1
=
sec (-30 )= sec (30 )
-1
=
csc = -2
3
sec (30 )= 1/ cos (30 )
3
tan = -
3
1/ cos ( 3 / 2 )= 2
3
cot = -
3
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The Correct Answer