Question

Given sin 0=7/4and angle 0 is in quadrant 1 what is the exact value of cos 0 in simplest form? Simplify all radics if needed

Answer 1

Answer: ¾

Explanation:

» From the trigonometric identities:

`{ \tt{ \sin {}^(2) \theta + \cos {}^(2) \theta = 1 }}`

» Substitute to the formular:

`{ \tt {( ( √(7) )/(4) )}^(2) + { \cos }^(2) \theta = 1 } \\ \\ { \tt{ (7)/(16) + { \cos}^(2) \theta = 1 }} \\ \\ { \tt{ \cos {}^(2) \theta = 1 - (7)/(16) }} \\ \\ { \tt{( \cos\theta) {}^(2) = (9)/(16) }} \\ \\ { \tt{ \sqrt{ {( \cos \theta}^(2)) } = \sqrt{( (9)/(16)) } }} \\ \\ { \tt{ \cos \theta = ( √(9) )/( √(16) ) }} \\ \\ { \boxed{ \tt{ \cos \theta = (3)/(4) }}}`