Trigonometry Questions?

Question

1)

sin(ß+11) = cos(63)

find ß

2)

if tan

Answer 1

1).

sin(β + 11⁰) = cos(63⁰).

Apply sin^-1 on each side.

sin^-1 [sin(β + 11⁰)] = sin^-1 [cos(63⁰)]

sin(sin^-1(x)) = x   for every x in the interval [-1, 1].

sin^-1(sin(x)) = x   for every x in the interval [ - π/2, π/2].

β + 11⁰ = sin^-1 [cos(63⁰)]

β + 11⁰ = sin^-1 [sin(90⁰ - 63⁰)]

β + 11⁰ = 90⁰ - 63⁰

β + 11⁰ = 27⁰

⇒ β = 27⁰ - 11⁰ = 16⁰.

Therefore, β = 16⁰.