Question

Use identities to find sin2Θ and cos2Θ, given cosΘ= -12/15 and sinΘ>0 PLZ HELP ASAP

Answer 1

see explanation

Explanation:

using the trigonometric identities

• sin2x = 2sinxcosx

• cos2x = 2cos²x - 1

• sin²x + cos²x = 1

sinx = ±
`√(1-cos^2x)`

= ±
`√(1-(-12/15)^2)`

= ±
`\sqrt{1-(144)/(225) }`

= ±
`\sqrt{(81)/(225) }` = ±
`(9)/(15)`

since sinΘ > 0 then sinΘ =
`(9)/(15)` =
`(3)/(5)`

sin2Θ = 2 ×
`(3)/(5)` × -
`(12)/(15)` = -
`(24)/(25)`

cos2Θ = 2 × (-
`(12)/(15)`)² - 1

= 2 ×
`(144)/(225)` - 1

=
`(288)/(225)` - 1 =
`(63)/(225)` =
`(7)/(25)`