Math  /  Trigonometry

QuestionUse the half-angle formula to find the exact value of cos(15)=\cos \left(15^{\circ}\right)= \square
Submit Question

Studdy Solution
Simplify the expression inside the square root:
cos(15)=±2+34\cos(15^\circ) = \pm \sqrt{\frac{2 + \sqrt{3}}{4}}
cos(15)=±2+32\cos(15^\circ) = \pm \frac{\sqrt{2 + \sqrt{3}}}{2}
Since 1515^\circ is in the first quadrant, where cosine is positive, we choose the positive value:
cos(15)=2+32\cos(15^\circ) = \frac{\sqrt{2 + \sqrt{3}}}{2}
The exact value of cos(15)\cos(15^\circ) is:
2+32\boxed{\frac{\sqrt{2 + \sqrt{3}}}{2}}

View Full Solution - Free
Was this helpful?

Studdy solves anything!

banner

Start learning now

Download Studdy AI Tutor now. Learn with ease and get all help you need to be successful at school.

ParentsInfluencer programContactPolicyTerms
TwitterInstagramFacebookTikTokDiscord