Question

Please help with my math problem! Thank you :)

Answer 1

cosΘ =
`(11)/(12)`

Explanation:

Using the trigonometric identity

sin²x + cos²x = 1 ⇒ cosx = ±
`√(1-sin^2x)`

Given

sinΘ =
`(√(23) )/(12)`, then

cosΘ = ±
`\sqrt{1-((√(23) )/(12) }`)² = ±
`\sqrt{1-(23)/(144) }` = ±
`\sqrt{(121)/(144) }` = ±
`(11)/(12)`

Since Θ is in first quadrant then cosΘ > 0

cosΘ =
`(11)/(12)`

Answer 2

cos Ф = 11/12

Explanation:

Given that:

sinФ =
`√(23)/12`

Putting in Pythagoras theorem:

(
`√(23)/12`)^2 + cos^2 Ф = 1

23/144 + cos^2 Ф = 1

Subtracting 23/144 on both sides:

cos^2 Ф = 1 - 23/144

By taking LCM

cos^2 Ф = (144 - 23)/144

cos^2 Ф = 121/144

Taking square root on both sides we get:

cos Ф = 11/12

I hope it will help you!