VERIFYING TRIGONOMETRIC IDENTITIES
Basic Identities Review
• The basic trigonometric identities consist of the reciprocal identities, quotient identities,
identities for negatives, and the Pythagorean identities.
• These identities were introduced in Chapter 5 Section 2, however in this chapter we are
going to review the basic identities and show how to use them to determine other
identities.
• The following slides consist of the basic identities summarized individually. These
should be memorized because they are going to be often used in the problems that follow.
Reciprocal Identities
• csc x = 1/ sin x Example: sin x = -½
Answer: csc x = 1/(-½)
= 1(-2/1)
= -2
• sec x = 1/ cos x Example: cos x = -√2/2
Answer: sec x = 1/ -√2/2
= 1(-2/√2)
= -2/ √2
• cot x = 1/ tan x Example: sin x = -½, and cos x = -√2/2
Answer: cot x = 1/ tan x
= 1/ (sin x/cos x)
= 1/ [(-½)/ (-√2/2)]
= 1/ [(-½ )(-2/√2)]
= 1/ (1/√2) = √2
Quotient Identities
• tan x = sin x/ cos x Example: sin x = 0, and cos x = -1
Answer: tan x = 0/-1
= 0
• cot x = cos x/ sin x Example: cos x = ½ , and sin x = √3/2
Answer: cot x = ½ / √3/2
= ½ (2/√3)
= 1/√3
by Shavana Gonzalez
