Mid-Chapter Quiz
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Consider using the Pythagorean Identity cos ^2 θ + sin ^2 θ= 1.
sin θ =4/5
We want to find the exact value of sin θ given that cos θ = 35. To do so, we will use one of the Pythagorean Identities.
cos ^2 θ +sin ^2 θ =1
Let's do it!
LHS^2=RHS^2
(a/b)^m=a^m/b^m
Calculate power
LHS+sin ^2 θ=RHS+sin ^2 θ
cos ^2 θ + sin ^2 θ= 1
LHS-9/25=RHS-9/25
Rewrite 1 as 25/25
Subtract fractions
Rearrange equation
sqrt(LHS)=sqrt(RHS)
sqrt(a/b)=sqrt(a)/sqrt(b)
Calculate root
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. Therefore, we will only keep the positive solution. sin θ =4/5