Question

The Pythagorean Identity states that(sin x)2 + (cos x)2 = 1Given sin theta = 7/10 find cos theta

Answer 1

Given that the Pythagorean identity states that

`\begin{gathered} sin^2x+cos^2x=1 \\ and,\sin\theta=(7)/(10),find,\cos\theta \end{gathered}`

By substituting the values, we will have

`\begin{gathered} s\imaginaryI n^2x+cos^2x=1 \\ ((7)/(10))^2+cos^2\theta=1 \\ (49)/(100)+cos^2\theta=1 \end{gathered}`

Collect similar terms by subtracting 49/100 from both sides

`\begin{gathered} (49)/(100)+cos^(2)\theta=1 \\ (49)/(100)-(49)/(100)+cos^2\theta=1-(49)/(100) \\ cos^2\theta=(100-49)/(100) \\ cos^2\theta=(51)/(100) \end{gathered}`

Square root both sides to calculate the value of cos θ

`\begin{gathered} cos^(2)\theta=(51)/(100) \\ \cos\theta=\sqrt{(51)/(100)} \\ \cos\theta=(√(51))/(10) \end{gathered}`

Hence,

The value of cos θ is

`\Rightarrow\cos\theta=(√(51))/(10)`