Write the first trigonometric function in terms of the second for theta in the given quadrant. sec⁡ theta,sin⁡ theta; theta in quadrant I.

potrzebag18

potrzebag18

Answered question

2023-02-11

Write the first trigonometric function in terms of the second for θ in the given quadrant. sec θ , sin θ ; θ in quadrant I.

Answer & Explanation

kistkalfljw

kistkalfljw

Beginner2023-02-12Added 6 answers

Find the first trigonometric function in terms of the second for θ in the given quadrant:
In light of the indicated quadrant,
secθ,sinθ;θ in quadrant I
We know that in quadrant I
sinθ>0cosθ>0
Based on trigonometric identities.
secθ=1cosθ......(1)
We know that,
sin2θ+cos2θ=1cos2θ=1-sin2θcosθ=1-sin2θ
Substituting the value of cosθ=1-sin2θ in the Equation (1)
secθ=11-sin2θ
Thus, the value of secθ is equal to 11-sin2θ.

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