Monday

March 2, 2015

March 2, 2015

Posted by **Joel** on Wednesday, May 8, 2013 at 12:57am.

Find the exact value of sin (omega-theta)

- PreCalc -
**Joel**, Wednesday, May 8, 2013 at 1:25amsorry that should be theta-omega not omega-theta

- PreCalc -
**Steve**, Wednesday, May 8, 2013 at 11:07amCleverly, you note that since

tanθ = cotω, ω = π/2-θ

Thus, θ-ω = θ-(π/2-θ) = π/2+2θ

sin(θ-ω) = -cos2θ = 2sin^θ-1

tanθ = 9/5, so

sinθ = 9/√106

sin(θ-ω) = 162/106 - 1 = 56/106

or, if you must exercise your sum/difference formulas,

sin(θ-ω) = sinθcosω-cosθsinω

tanθ = 9/5, so

sinθ = 9/√106

cosθ = 5/√106

cotω = 9/5, so

sinω = 5/√106

cosω = 9/√106

sin(θ-ω) = 9/√106 * 9/√106 - 5/√106 * 5/√106 = 56/106

**Answer this Question**

**Related Questions**

Trigonometry - Prove that sin^2(Omega) - Cos^2(Omega) / tan(Omega) sin(Omega) + ...

Algebra II - Multiple Choice (theta) means the symbol 0 with the dash in it. 1.)...

Precalculus check answers help! - 1.) Find an expression equivalent to sec theta...

Precalculus check answers help! - 1.) Find an expression equivalent to sec theta...

Trig - 1. Establish the identity: sin(theta+3pi/2)=-cos(theta) 2. Find the exact...

Math - 1. Let (-7, 4) be a point on the terminal side of (theta). Find the exact...

I dont think drawing a picture will help me drwls - Which expression is ...

trig - If sin theta is equal to 5/13 and theta is an angle in quadrant II find ...

easy trig - If sin(theta)=[sqrt(70)]/7 and theta is in Quadrant two, find the ...

simple trig - If sin(theta)=[sqrt(70)]/7 and theta is in Quadrant two, find the ...