Question

Please please please help with my math problem. Thanks :)

Answer 1

cosΘ =
`(√(51) )/(10)`

Explanation:

Using the trigonometric identity

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

Given

sinΘ =
`(7)/(10)`, then

cosΘ = ±
`√(1-(7/10)^2)` = ±
`\sqrt{1-(49)/(100) }` = ±
`\sqrt{(51)/(100) }` = ±
`(√(51) )/(10)`

Since Θ is in first quadrant then cosΘ > 0

cosΘ =
`(√(51) )/(10)`

Answer 2

`√(51)/10`

Explanation:

Given that:

sinФ = 7/10

Putting in Pythagoras theorem:

(7/10)^2 + cos^2 Ф = 1

49/100 + cos^2 Ф = 1

Subtracting 49/100 on both sides:

cos^2 Ф = 1 - 49/100

By taking LCM

cos^2 Ф = (100 - 49)/100

cos^2 Ф = 51/100

Taking square root on both sides we get:

cos Ф =
`√(51)`/100

I hope it will help you!