**Unformatted text preview: **x and
sin(θ) = y in Deﬁnition 10.2, it is customary to rephrase the remaining four circular functions in
terms of cosine and sine. The following theorem is a result of simply replacing x with cos(θ) and y
with sin(θ) in Deﬁnition 10.2.
Theorem 10.6. Reciprocal and Quotient Identities:
• sec(θ) = 1
, provided cos(θ) = 0; if cos(θ) = 0, sec(θ) is undeﬁned.
cos(θ) • csc(θ) = 1
, provided sin(θ) = 0; if sin(θ) = 0, csc(θ) is undeﬁned.
sin(θ) • tan(θ) = sin(θ)
, provided cos(θ) = 0; if cos(θ) = 0, tan(θ) is undeﬁned.
cos(θ) • cot(θ) = cos(θ)
, provided sin(θ) = 0; if sin(θ) = 0, cot(θ) is undeﬁned.
sin(θ) It is high time for an example.
Example 10.3.1. Find the indicated value, if it exists.
1. sec (60◦ ) 2. csc 7π
4 π
4. tan (θ), where θ is any angle coterminal with 32 .
√
5. cos (θ), where csc(θ) = − 5 and θ is a Quadrant IV angle. 6. sin (θ), where tan(θ) = 3 and θ is a Quadrant III angle.
1 Compare this with the deﬁnition given in Section 2.1. 3. cot(3) 10.3 The Six Circular Functions and Fu...

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