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2 As we shall see shortly, when solving equations involving secant and cosecant, we usually convert back to cosines
and sines. However, when solving for tangent or cotangent, we usually stick with what we’re dealt. 638 Foundations of Trigonometry
Tangent and Cotangent Values of Common Angles
0◦ 0 45◦
3 √ undeﬁned π
2 cot(θ) √ 0 30◦ tan(θ) 0 3
3 Coupling Theorem 10.6 with the Reference Angle Theorem, Theorem 10.2, we get the following.
Theorem 10.7. Generalized Reference Angle Theorem. The values of the circular functions
of an angle, if they exist, are the same, up to a sign, of the corresponding circular functions of
its reference angle. More speciﬁcally, if α is the reference angle for θ, then: cos(θ) = ± cos(α),
sin(θ) = ± sin(α), sec(θ) = ± sec(α), csc(θ) = ± csc(α), tan(θ) = ± tan(α) and cot(θ) = ± cot(α).
The choice of the (±) depends on the quadrant in which the terminal side of θ lies.
We put Theorem 10.7 to good use in the following example.
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