Still have math questions?

Ask our expert tutors
Trigonometry
Question

Given \(\sin \theta = - \frac { 1 } { 4 }\) and an...

Given \(\sin \theta = - \frac { 1 } { 4 }\) and angle \(\theta\) is in Quadrant III, what is the exact value of \(\cos \theta\) in simplest form? Simplify all radicals if needed. 

Answer: \(\cos \theta = \) 

Answer

\(\sin \theta = - \frac { 1 } { 4 } \) 

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

\( \cos \theta = \pm \sqrt { 1 - ( - \frac { 1 } { 4 } ) ^ { 2 } } \) 

\( \theta i s \operatorname { in } \theta \frac { \pi } { 11 } \) 

\( \therefore \cos \theta < 0 \) 

\( \therefore \cos \theta = - \sqrt { \frac { 15 } { 16 } } = - \frac { \sqrt { 15 } } { 4 }\) 

Solution
View full explanation on CameraMath App.