January 29, 2015
2-4
Basic Trigonometric
Identities
Example 1
Reciprocal Identities
Quotient Identities
Use a reciprocal identity to find the function value indicated.
a) If sin θ = -3/7, find csc θ
b) If cos θ = 0.8, find sec θ
Example 2
Use a quotient identity to find the function value indicated.
Rationalize denominators if necessary.
a) If sin θ = -½ and cos θ = √3 ⁄ 2, find cot θ.
b) If sin θ = 4/5 and cos θ = -3/5, find tan θ.
Pythagorean Identities
January 29, 2015
Example 3
Example 3 - cont
Use a Pythagorean identity to find the function value indicated.
Rationalize denominators if necessary.
Use a Pythagorean identity to find the function value indicated.
Rationalize denominators if necessary.
a) If sin θ = -3/5 and the terminal side of θ lies in quadrant III, find cos θ.
c) If secθ = -√61 / 5 and the terminal side of θ lies in quadrant II, find sinθ.
b) If tan θ = -5 and the terminal side of θ lies in quadrant II, find sec θ.
Example 4
Example 4
Use appropriate identities to find the function value indicated.
Rationalize denominators if necessary.
Use appropriate identities to find the function value indicated.
Rationalize denominators if necessary.
a) Find sin θ and cos θ if tan θ = -¾ and the terminal side of θ lies in QII
a) Find sin θ and cos θ if tan θ = -¾ and the terminal side of θ lies in QII
b) Find sin θ and cos θ if tan θ = -⅔ and the terminal side of θ lies in QIV
b) Find sin θ and cos θ if tan θ = -⅔ and the terminal side of θ lies in QIV
Example 5
Example 5
Simplify each of the following expressions, if possible. Leave all
answers in terms of sin θ and cos θ.
Simplify each of the following expressions, if possible. Leave all
answers in terms of sin θ and cos θ.
a) cscθtanθ
b) cot2θ - csc2θ
a) cscθtanθ
b) cot2θ - csc2θ
c) sec θ - cos θ
c) sec θ - cos θ
January 29, 2015
d) csc θ ⁄ cot θ
e) (sin θ - cos θ)2