Solve -sin 20° sin 40° sin 60° sin 80°sin 20° cos 30° sin 40°

  • Context: Undergrad 
  • Thread starter Thread starter Kartik.
  • Start date Start date
  • Tags Tags
    Cos Sin
Click For Summary
SUMMARY

The expression -sin 20° sin 40° sin 60° sin 80° is mathematically equivalent to sin 20° cos 30° sin 40° cos 10°, with both sides simplifying to 3/16. This conclusion is established through trigonometric identities and simplifications. The discussion confirms that both expressions yield the same value, reinforcing the principles of trigonometric functions.

PREREQUISITES
  • Understanding of trigonometric identities
  • Familiarity with angle measurements in degrees
  • Basic algebraic manipulation skills
  • Knowledge of sine and cosine functions
NEXT STEPS
  • Study trigonometric identities and their applications
  • Explore the unit circle and angle relationships
  • Learn about the properties of sine and cosine functions
  • Practice solving trigonometric equations
USEFUL FOR

Students, educators, and anyone interested in enhancing their understanding of trigonometric functions and identities in mathematics.

Kartik.
Messages
55
Reaction score
1
Solve -
sin 20° sin 40° sin 60° sin 80°

sin 20° cos 30° sin 40° cos 10°
hmm...?
 
Mathematics news on Phys.org


Err...this is the general math column!
 


Yes, they are both equal to 3/16 and this is "general math". What is your point?
 

Similar threads

Undergrad Is it possible to express cos(40) as a radical?
  • · Replies 4 ·
Replies
4
Views
3K
MHB Solving Trig Identity: Sin[1/2 sin^−1 (x)] = 1/2 X (sqr(1+x) –sqr(1-x))
  • · Replies 2 ·
Replies
2
Views
1K
Undergrad Linear combination of sin and cos
  • · Replies 1 ·
Replies
1
Views
2K
MHB Lowest Positive $p$: Solving $\cos(p\sin \, x) = \sin (p\cos\, x)$
  • · Replies 4 ·
Replies
4
Views
2K
MHB Solve sin(x)-1=cos(x): Step-by-Step Guide
  • · Replies 6 ·
Replies
6
Views
3K
MHB Solve the equation cos^8θ+sin^8θ−2(1−cos^2θsin^2θ)^2+1=0
  • · Replies 4 ·
Replies
4
Views
2K
MHB How to Solve the Trigonometric Equation 6*Sin^2(x) - 3*Sin^2(2x) + Cos^2(x) = 0?
  • · Replies 6 ·
Replies
6
Views
3K
MHB Proving a Fraction Inequality of Sin and Cos | $\pi/2$
  • · Replies 3 ·
Replies
3
Views
2K
Proving Sin(120) = Sin(60) with Trigonometry
  • · Replies 3 ·
Replies
3
Views
3K
MHB Find cos theta and tan theta using sin theta
  • · Replies 4 ·
Replies
4
Views
8K