sinx+cosx=5/4,find sin2x,cos2x,tg2x
- print Print
- list Cite
Expert Answers
calendarEducator since 2011
write5,349 answers
starTop subjects are Math, Science, and Business
You should raise to square the expression `sin x + cos x = 5/4` such that:
`(sin x + cos x)^2 = (5/4)^2`
`sin^2 x + 2 sin x cos x + cos^2 x = 25/16`
Since `sin^2 x + cos^2 x = 1` yields:
`1 + 2 sin x cos x = 25/16 => 2 sin x cos x = 25/16 - 1`
Using trigonometric identities yields `2 sin x cos x = sin 2x ` such that:
`sin 2x = (25-16)/16 => sin 2x = 9/16`
You may evaluate `cos 2x` using fundamental formula of trigonometry such that:
`sin^2 2x + cos^2 2x = 1 => cos 2x = +-sqrt(1 - sin^2 2x)`
`cos 2x = +-sqrt(1 - 81/256) => cos 2x = +-sqrt175/256 => cos 2x = +-5sqrt7/16`
You may evaluate `tan 2x` using the identity `tan alpha = sin alpha/cos alpha` such that:
`tan 2x = (sin 2x)/(cos 2x) => tan 2x = (9/16)/(+-5sqrt7/16)`
`tan 2x +-9/(5sqrt7) => tan 2x = +-9sqrt7/35`
Hence, evaluating `sin 2x, cos 2x ` and `tan 2x` , under the given conditions, yields `sin 2x = 9/16 , cos 2x = +-5sqrt7/16, tan 2x = +-9sqrt7/35.`
Related Questions
- calculate: sinx+sin2x+sin3x=1+cosx+cos2x ∈(pi/2;5pi/6)
- 1 Educator Answer
- Please solve the equation sinx+cosx-sin2x+cos2x-cos3x=1.
- 1 Educator Answer
- Prove the identity (sinx)^2 - (cosx)^2 = (sinx)^4 - (cosx)^4
- 2 Educator Answers
- Solve: (sinx)^4 + (cosx) ^4 = 1
- 1 Educator Answer
- if sinx = 3/5 calculate cosx , tan, x and secx
- 1 Educator Answer