Question

Sin theta =1/10 and Angle theta is in Quadrant 4

Find: • sin2theta:
• Cos2theta:
• Tan2theta:

Answer 1

sin(2Θ) = -0.199

cos(2Θ) = 0.98

tan(2Θ) = -0.203

Explanation:

sin(Θ) = -0.1

therefore Θ = -5.74° because Θ is in the fourth quadrant.

cos(Θ) =
`√(1 - sin^2\theta) = √(1 - (0.1)^2) = √(0.99) = 0.995`

i) sin(2Θ) = 2sin(Θ)cos(Θ) = 2
`*` (-0.1)
`*` 0.995 = -0.199

ii) cos(2Θ) =
`cos^(2) \theta - sin^(2) \theta = (0.995)^(2) - (-0.1)^(2) = 0.99 -0.01 = 0.98`

iii) tan(2Θ) =
`(-0.199)/(0.98) = -0.203`