Mid-Chapter Quiz
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Consider using the Pythagorean Identity tan ^2 θ + 1 = sec ^2 θ.
tan θ =sqrt(7)/3
We want to find the exact value of tan θ given that sec θ = 43. To do so, we will use one of the Pythagorean Identities.
tan ^2 θ + 1 = sec ^2 θ
Let's do it!
LHS^2=RHS^2
(a/b)^m=a^m/b^m
Calculate power
sec ^2 θ= tan ^2 θ+1
Be aware that we are told that θ lies between 0^(∘) and 90^(∘). Therefore, θ is in Quadrant I.
In this quadrant, the sine of θ is positive and the cosine of θ is positive. Since tan θ= sin θcos θ, the sign of tan θ is positive in this quadrant. Therefore, we will only keep the positive solution. tan θ =sqrt(7)/3