Trigonometry: Half-Angle Identities
Read this topicExplanations 3
- We have the following double-angle identity: cos(2A)=cos2A−sin2A=2cos2A−1=1−2sin2A\cos(2A) = \cos^2 A - \sin^2 A = 2\cos^2 A - 1 = 1 - 2\sin^2 Acos(2A)=cos2A−sin2A=2cos2A−1…
By Sujay Kazi
- (Video) Half Angle Formulas & Identities - Evaluating Trigonometric Expressions by The Organic Chemistry Tutor Check out this video by the Organic Chemistry Tutor! Let's follow …
By Trisha
- Trigonometry: Half-Angle Identities There are six negative angle identities you need to memorize! Negative angle identities Co-function identities Angle and sum differences iden…
By Trisha, Anusha Rahman
Problems 8
- In a 15-75-90 triangle, the hypotenuse has length 1. Find the length of the side opposite the 15 degree angle.
- (ARML 2014 Team Round #7) Compute: sin24∘+sin28∘+sin212∘+...+sin2176∘.\sin^2 4^{\circ} + \sin^2 8^{\circ} + \sin^2 12^{\circ} + ... + \sin^2 176^{\circ}.sin24∘+sin28∘+sin212…
- If aaa and bbb are positive integers such that 8+32+768=acosπb,\sqrt{8 + \sqrt{32 + \sqrt{768}}} = a \cos \frac{\pi}{b},8+32+768=acosbπ, compute the ordered pair (a,b)(a, b…
- If csc(x)=7\csc(x)=7csc(x)=7 and 90∘<x<180∘90^{\circ}<x<180^{\circ}90∘<x<180∘, then find the exact value for sin(x2)\sin(\frac x2)sin(2x)
- If csc(x)=7\csc(x)=7csc(x)=7 and 90∘<x<180∘90^{\circ}<x<180^{\circ}90∘<x<180∘, then find the exact value for cos(x2)\cos(\frac x2)cos(2x)
- If csc(x)=7\csc(x)=7csc(x)=7 and 90∘<x<180∘90^{\circ}<x<180^{\circ}90∘<x<180∘, then find the exact value for tan(x2)\tan(\frac x2)tan(2x)
- Find the exact value of the following expression using half-angle formula(s): sin3π8\sin\frac{3\pi}{8}sin83π
- Find the exact value of the following expression using half formula(s): cos7π12\cos\frac{7\pi}{12}cos127π